Defendants Robert Lillis, Leonard Pas-tore, Anthony DiLullo, and Mary Fish-MacDonald appeal from so much of an order of the United States District Court for the District of Connecticut, José A. Cabranes, Judge, as denied their motion for summary judgment dismissing claims against them by plaintiff Anthony Golino under 42 U.S.C. § 1983 (1988) for malicious prosecution. Appellants moved for summary judgment on the grounds that (1) a state-court finding during the prior criminal proceeding collaterally estops Golino from litigating in the present case the issue of whether there was probable cause to prosecute him, and (2) as police officers, they enjoy qualified immunity from the present suit. The district court denied appellants’ motion on the grounds that (1) collateral estoppel was inappropriate because Golino had not had a sufficient opportunity in the prior proceeding to litigate the probable cause question, and (2) there were genuine issues of material fact to be tried with respect to the immunity defense. On appeal, appellants contend that the district court erred in concluding (1) that Golino did not have an adequate opportunity to litigate the question of probable cause, and (2) that any existing questions of fact with respect to probable cause are material. For the reasons below, we reject both contentions and affirm the order of the district court.

I. BACKGROUND

The present action arises out of an 11-year investigation by the City of New Haven Police Department into the 1973 murder of Concetta (“Penny”) Serra. Lillis, a police sergeant, supervised the investigation. DiLullo and Pastore, police detectives, and Fish-MacDonald, a police officer, had primary operational responsibility for the investigation. In July 1984, Golino was arrested pursuant to an arrest warrant and charged with the murder.

In August 1984, following a preliminary evidentiary hearing held pursuant to state law (“1984 state hearing”), Connecticut Superior Court Judge Frank Kinney found probable cause to support the murder charge. At that hearing, Judge Kinney permitted Golino’s counsel to cross-examine the state’s witnesses and to make a brief written offer of proof, but he denied Goli-no’s request to introduce evidence. In May 1987, just prior to the scheduled start of Golino’s trial for murder, a court-ordered blood test revealed that Golino’s blood type did not match that of the killer. The charges against Golino were then dismissed.

In January 1988, Golino commenced the present action against appellants and several other defendants. To the extent pertinent here, he asserted claims against appellants under § 1983 for malicious prosecution. After a period of discovery, appellants moved for summary judgment dismissing these claims on the grounds that (1) as police officers, they were entitled to qualified immunity because there existed no genuine issue of fact as to the existence of probable cause to arrest and try Golino, or (2) Judge Kinney’s probable cause determination precluded Golino from relitigating that issue in the present case.

In a ruling reported at 761 F.Supp. 962 (1991), the district court denied this motion, stating that “the record as it currently stands contains evidence from which a reasonable jury might infer that plaintiff was maliciously prosecuted.” Id. at 964. The court noted that in order to establish a[*867] § 1983 claim for malicious prosecution, a plaintiff must show, inter alia, that the prosecution was without probable cause. See Conway v. Village of Mount Kisco, 750 F.2d 205, 214 (2d Cir.1984) (state law defines elements of a malicious prosecution claim asserted under § 1983, see 42 U.S.C. § 1988 (1988)); McGann v. Allen, 105 Conn. 177, 185, 134 A. 810, 813 (1926) (absence of probable cause is one element of malicious prosecution claim under Connecticut law). As to appellants’ defense of issue preclusion, the court found that the authorities cited for the proposition that a state-court probable cause hearing generally has collateral estoppel effect did not establish that proposition. In addition, noting that it was undisputed that Golino had not been permitted to present evidence at the 1984 state hearing, the court concluded that he had not been given an adequate opportunity at that hearing to contest probable cause. Thus, the court concluded that litigation here of the issue of probable cause was not foreclosed by principles of collateral estoppel.

As to the merits of the probable cause question, the court concluded that there existed genuine issues of material fact because the affidavit leading to the warrant for Golino’s arrest, and to his subsequent prosecution, contained false statements and made numerous material omissions. To begin with, Golino was connected to the Serra murder principally by statements that the police attributed to his former wife, Joyce Carasone Lupone (from whom he had separated in 1980, and who testified at the 1984 state hearing that she hated Golino and would do anything she could to keep him from getting custody of their son), whom the police knew to be involved in acrimonious divorce proceedings with Golino. The warrant affidavit quoted Lupone as stating that on more than one occasion Golino had made incriminating remarks to her, i.e., threatening to do to her “the same ... as he had done to Penny Serra.” The affidavit did not disclose, however, that Lupone had also made statements to the police that were inconsistent with the statements it attributed to her, and it omitted mention of the fact that at one time Lupone told the police that Golino never made the quoted statements. The affidavit also stated that an informant, Neil Russo, told police that Golino had dated Serra. The district court noted the probable falsity of this statement in light of Russo’s deposition testimony in the present case that he had never made this statement to the police and that when they interviewed him, he would “say one thing and they put down another thing.”

The court also noted that a number of other evidently pertinent facts had been omitted from the arrest warrant affidavit. For example, the affidavit described the killer only as “a white male wearing a light colored shirt and dark trousers, carrying a shiney [sic] object in his hand,” notwithstanding the fact that several eyewitnesses had given descriptions in considerably greater detail. Thus, one eyewitness described the killer as “approximately 5'8" tall, 150 to 160 pounds [with a] slim build”; another stated that he had a “thin face” and “skinny arms”; a third eyewitness also described the killer as having a “thin face.” The significance of these omissions was that Golino, at the time of Serra’s death, weighed approximately 215 pounds. All three of these eyewitnesses also stated that the killer had no mustache. Golino, at the time, had a mustache. A fourth eyewitness had described the killer as having a mustache; but that eyewitness had, within hours of the murder, affirmatively identified another person, from both a photo array and a lineup, as the killer, and the person identified was Serra’s boyfriend. Further, the affidavit did not mention that the killer’s blood type was known but that the police had not bothered to seek a court order for a test to determine Golino’s blood type. It also failed to mention that fingerprints on Serra’s car that the police strongly believed to belong to her killer did not match the fingerprints of Golino. DiLullo testified at his deposition in the present case that it was his general practice to omit exculpatory information from affidavits submitted in support of applications for warrants.

[*868] The district court concluded that it could not rule as a matter of law that it was “ ‘objectively reasonable for [appellants] to believe that they were acting in a fashion that did not violate [Golino’s] established federally protected right[s].’ ” 761 F.Supp. at 971-72 (quoting Hurlman v. Rice, 927 F.2d 74, 79 (2d Cir.1991)). Accordingly, an order was entered denying so much of appellants’ motion as sought dismissal of the malicious prosecution claims. This appeal followed.

II. DISCUSSION

On appeal, appellants pursue their contentions that they were entitled to summary judgment dismissing the malicious prosecution claims on grounds of collateral estoppel and qualified immunity. For the reasons below, we conclude that the district court properly denied appellants’ motion. We note first, however, a question as to appellate jurisdiction.

A. Appellate Jurisdiction

The denial of summary judgment is ordinarily not an appealable “final decision” within the meaning of 28 U.S.C. § 1291 (1988). A district court’s denial of a summary judgment motion that is based upon a substantial claim of qualified immunity, however, is immediately appealable where the district court has rejected the defense as a matter of law. See, e.g., Mitchell v. Forsyth, 472 U.S. 511, 530, 105 S.Ct. 2806, 2817, 86 L.Ed.2d 411 (1985); Magnotti v. Kuntz, 918 F.2d 364, 367 (2d Cir.1990). Where the district court has ruled that adjudication of the immunity defense requires resolution of genuinely disputed questions of material fact, the denial of summary judgment is not immediately appealable. See, e.g., Mitchell v. Forsyth, 472 U.S. at 530, 105 S.Ct. at 2817; Kaminsky v. Rosenblum, 929 F.2d 922, 926 (2d Cir.1991); Hurlman v. Rice, 927 F.2d at 79; Langley v. Coughlin, 888 F.2d 252, 254 (2d Cir.1989). Thus, we have jurisdiction to review appellants’ immunity defense only to the extent that it can be decided as a matter of law. These principles have significance here in two respects.

Leaving aside for the moment appellants’ claim of collateral estoppel, the district court ruled that the merits of appellants’ claim of qualified immunity could not be decided on summary judgment because there were material issues of facts to be determined with respect to (a) whether there was probable cause, and (b) whether it was objectively reasonable for appellants to believe they had probable cause. Since the court ruled that the resolution of these probable cause issues involved questions of fact, the ruling is not, in principle, immediately appealable.

In contrast, there are no questions of fact to be determined with respect to the collateral estoppel argument. There is no dispute as to what occurred at the state-court hearing, or as to what questions were before the court, or as to what issues were necessarily decided. Thus, the district court’s ruling that, in light of the undisputed facts, there is no collateral estoppel is a ruling on a question of law. This ruling has twofold significance to appellants' qualified immunity defense, for if appellants had probable cause to arrest and prosecute Golino, (a) there would have been no violation of his constitutional rights, see Siegert v. Gilley, — U.S. -, 111 S.Ct. 1789, 1793, 114 L.Ed.2d 277 (1991) (defendant entitled to qualified immunity where, as a matter of law, plaintiff cannot prove a constitutional violation), and (b) it would have been objectively reasonable for them to believe that those actions did not violate his constitutional rights. Accordingly, since the rejection of the collateral estoppel argument was a purely legal ruling and affects whether qualified immunity is available as a matter of law, we have jurisdiction to review the denial of summary judgment on the collateral estoppel ground.

As noted above, the court's ruling that the merits of the probable cause issue turn on questions of fact was not, in and of itself, appealable. However, where we have jurisdiction to consider some questions on appeal, we may exercise our discretion to take pendent jurisdiction over related questions. See, e.g., San Filippo v. United States Trust Co. of New York, 737[*869] F.2d 246, 255 (2d Cir.1984) (“once we have taken jurisdiction over one issue in a case, we may, in our discretion, consider otherwise nonappealable issues in the case as well, where ‘[tjhere is sufficient overlap in the factors relevant to [the appealable and nonappealable] issues to warrant our exercising plenary authority over [the] appeal’ ”) (quoting Sanders v. Levy, 558 F.2d 686, 643 (2d Cir.1976), rev’d on other grounds sub nom. Oppenheimer Fund, Inc. v. Sanders, 437 U.S. 340, 98 S.Ct. 2380, 57 L.Ed.2d 253 (1978)), cert. denied, 470 U.S. 1035, 105 S.Ct. 1408, 84 L.Ed.2d 797 (1985). Given the close relationship between the collateral estoppel issue, i.e., whether Golino had an adequate opportunity to contest the existence of probable cause, and the merits of the probable cause issues, we will exercise our discretion in this case to review the district court’s ruling that there exist material questions of fact as to the existence of probable cause and the objective reasonableness of any belief on the part of appellants that there existed probable cause.

B. The Collateral Estoppel Argument

Pursuant to 28 U.S.C. § 1738 (1988), the federal courts “must give to a state-court judgment the same preclusive effect as would be given that judgment under the law of the State in which the judgment was rendered.” Migra v. Warren City School District Board of Education, 465 U.S. 75, 81, 104 S.Ct. 892, 896, 79 L.Ed.2d 56 (1984). This rule applies to determine the preclusive effect of a state court judgment on a subsequent suit in federal court brought pursuant to § 1983. See Allen v. McCurry, 449 U.S. 90, 101 S.Ct. 411, 66 L.Ed.2d 308 (1980); Temple of the Lost Sheep, Inc. v. Abrams, 930 F.2d 178, 183 (2d Cir.), cert. denied, — U.S. -, 112 S.Ct. 193, 116 L.Ed.2d 153 (1991). Nonetheless, “[cjollat-eral estoppel does not apply where the party against whom an earlier court decision is asserted did not have a full and fair opportunity to litigate the claim or issue decided by the first court.” Allen v. McCurry, 449 U.S. at 101, 101 S.Ct. at 418.

Under Connecticut law, “ ‘[f]or an issue to be subject to collateral estoppel, [1] it must have been fully and fairly litigated in the first action. [2] It also must have been actually decided and [3] the decision must have been necessary to the judgment.’ ” Aetna Casualty and Surety Co. v. Jones, 220 Conn. 285, 296, 596 A.2d 414, 421 (1991) (quoting Virgo v. Lyons, 209 Conn. 497, 501, 551 A.2d 1243, 1245 (1988)); P.X. Restaurant, Inc. v. Town of Windsor, 189 Conn. 153, 454 A.2d 1258, 1262 (1983). As to the first condition, the only one of the three at issue here, the Connecticut Supreme Court has explained that “[t]he requirement of full and fair litigation ensures fairness, which is a ‘crowning consideration’ in collateral estoppel cases.” Aetna Casualty and Surety Co. v. Jones, 220 Conn. at 306, 596 A.2d at 425. Thus, “if the nature of the hearing carries procedural limitations that would not be present at a later hearing, the party might not have a full and fair opportunity to litigate.” Id. at 306, 596 A.2d at 426; see also Bailey v. Andrews, 811 F.2d 366, 370 (7th Cir.1987) (finding of probable cause in state-court hearing, at which suspect was not allowed to present evidence or cross-examine witnesses, not given preclusive effect in subsequent § 1983 suit); Coogan v. City of Wixom, 820 F.2d 170, 175 (6th Cir.1987) (state-court finding of probable cause given pre-clusive effect in subsequent § 1983 suit because prior proceeding, at which suspect had a right to call witnesses and cross-examine witnesses, afforded him a full and fair opportunity to litigate the issue of probable cause).

We think the district court was correct in its assessment that, for collateral estoppel purposes, the 1984 state hearing entailed procedural limitations that curtailed Golino’s efforts to secure the full and fair litigation of the probable cause issue. The purpose of such a hearing is generally the evaluation of the “sufficiency” of the evidence to constitute probable cause, not the “integrity” of the evidence. See, e.g., Schertz v. Waupaca County, 875 F.2d 578, 581 (7th Cir.1989); Bailey v. Andrews, 811 F.2d at 369-70. Thus, at such a hearing under Connecticut law, the suspect apparently has no right to call any witnesses or[*870] to introduce any evidence of his own. Nor did the state court exercise discretion to permit Golino to call witnesses or offer evidence. Rather, he was limited to cross-examining the state’s witnesses and submitting a written offer of proof identifying witnesses and evidence he wished to present. Further, in connection with the preliminary hearing, Golino had no access to the police investigative file. As has transpired in the present action, that file contained numerous items of evidence that could have been used to cross-examine the police officers who testified and to create substantial questions about the existence of probable cause to prosecute Golino.

Given (a) the substantial showing in the present case that appellants’ presentations in support of probable cause contained numerous significant misstatements and omissions, and (b) the limitations on Goli-no’s ability to present his own evidence and to gain access to undisclosed significant facts known to the police in order to cross-examine the state’s witnesses, we conclude that the 1984 state hearing did not provide Golino a full and fair opportunity, for collateral estoppel purposes, to litigate the issue of probable cause. Accordingly, the district court properly ruled that the probable cause decision of Judge Kinney should not be given preclusive effect.

C. The Merits of the Qualified Immunity Defense

The qualified or “good faith” immunity enjoyed by police officers shields them from personal liability for damages “insofar as their conduct does not violate clearly established statutory or constitutional rights of which a reasonable person would have known,” Harlow v. Fitzgerald, 457 U.S. 800, 818, 102 S.Ct. 2727, 2738, 73 L.Ed.2d 396 (1982); see also Hurlman v. Rice, 927 F.2d at 78; Robison v. Via, 821 F.2d 913, 920 (2d Cir.1987), or insofar as it was objectively reasonable for them to believe that their acts did not violate those rights, see Anderson v. Creighton, 483 U.S. 635, 638, 107 S.Ct. 3034, 3038, 97 L.Ed.2d 523 (1987); Malley v. Briggs, 475 U.S. 335, 341, 106 S.Ct. 1092, 1096, 89 L.Ed.2d 271 (1986); Hurlman v. Rice, 927 F.2d at 78; Calamia v. City of New York, 879 F.2d 1025, 1035 (2d Cir.1989). The right not to be arrested or prosecuted without probable cause has, of course, long been a clearly established constitutional right. Probable cause to arrest exists when the authorities have knowledge or reasonably trustworthy information sufficient to warrant a person of reasonable caution in the belief that an offense has been committed by the person to be arrested. Dunaway v. New York, 442 U.S. 200, 208 n. 9, 99 S.Ct. 2248, 2254 n. 9, 60 L.Ed.2d 824 (1979). An arresting officer is entitled to qualified immunity from a suit for damages on a claim for arrest without probable cause if either (a) it was objectively reasonable for the officer to believe that probable cause existed, or (b) officers of reasonable competence could disagree on whether the probable cause test was met. See Malley v. Briggs, 415 U.S. at 341, 106 S.Ct. at 1096; Robison v. Via, 821 F.2d at 921. In order to be entitled to summary judgment on such a defense, the officer must adduce sufficient facts that no reasonable jury, looking at the evidence in the light most favorable to, and drawing all inferences most favorable to, the plaintiff, could conclude that it was objectively unreasonable for the officer to believe that probable cause did not exist. See id.

Normally, the issuance of a warrant by a neutral magistrate, which depends on a finding of probable cause, creates a presumption that it was objectively reasonable for the officers to believe that there was probable cause, see United States v. Ventresca, 380 U.S. 102, 109, 85 S.Ct. 741, 746, 13 L.Ed.2d 684 (1965), and a plaintiff who argues that a warrant was issued on less than probable cause faces a heavy burden, see, e.g., Rivera v. United States, 928 F.2d 592, 602 (2d Cir.1991) (search warrant). In order to mount such a challenge, the plaintiff must make a “substantial preliminary showing” that the affi-ant knowingly and intentionally, or with reckless disregard for the truth, made a false statement in his affidavit and that the allegedly false statement was “necessary to the finding of probable cause.” Franks [*871] v. Delaware, 438 U.S. 154, 155-56, 98 S.Ct. 2674, 2676, 57 L.Ed.2d 667 (1978); see Magnotti v. Kuntz, 918 F.2d at 368 (Franks standard, established with respect to suppression hearings in criminal proceedings, also defines scope of qualified immunity in civil rights actions). Intentional or reckless omissions of material information, like false statements, may serve as the basis for a Franks challenge, see United States v. Campino, 890 F.2d 588, 592 (2d Cir.1989), cert. denied, 494 U.S. 1068, 110 S.Ct. 1787, 108 L.Ed.2d 788 (1990), and recklessness may be inferred where the omitted information was critical to the probable cause determination, see Rivera v. United States, 928 F.2d at 604; DeLoach v. Bevers, 922 F.2d 618, 622 (10th Cir.1990), cert. denied, — U.S. -, 112 S.Ct. 65, 116 L.Ed.2d 41 (1991); Hale v. Fish, 899 F.2d 390, 400 (5th Cir.1990); United States v. Reivich, 793 F.2d 957, 961 (8th Cir.1986). Where an officer knows, or has reason to know, that he has materially misled a magistrate on the basis for a finding of probable cause, as where a material omission is intended to enhance the contents of the affidavit as support for a conclusion of probable cause, see generally, Rivera v. United States, 928 F.2d at 605; United States v. Strini, 658 F.2d 593, 597 (8th Cir.1981), the shield of qualified immunity is lost, see Malley v. Briggs, 475 U.S. at 344-45, 106 S.Ct. at 1097-98 (adopting standard set in United States v. Leon, 468 U.S. 897, 923, 104 S.Ct. 3405, 3420, 82 L.Ed.2d 677 (1984), as proper standard for objective reasonableness for qualified immunity purposes). An officer can “have no reasonable grounds for believing that [a] warrant was properly issued” “[i]f the magistrate or judge in issuing a warrant was misled by information in an affidavit that the affiant knew was false or would have known was false except for his reckless disregard of the truth,” United States v. Leon, 468 U.S. at 923, 104 S.Ct. at 3421.

Whether an item of information is material or not is, in the context of a motion for summary judgment, a mixed question of law and fact. See, e.g., TSC Industries, Inc. v. Northway, Inc., 426 U.S. 438, 450, 96 S.Ct. 2126, 2132, 48 L.Ed.2d 757 (1976). The legal component depends on whether the information is relevant to a given question in light of the controlling substantive law. Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248, 106 S.Ct. 2505, 2510, 91 L.Ed.2d 202 (1986). The factual component requires an inference as to whether the information would likely be given weight by a person considering that question. TSC Industries, Inc. v. Northway, Inc., 426 U.S. at 450, 96 S.Ct. at 2132.

The district court properly applied these principles in the present case to deny appellants’ motion for summary judgment. Appellants contend that they are entitled to immunity as a matter of law because it would have been objectively reasonable for them to believe that if the warrant affidavit were corrected to disclose all of the omitted information and to eliminate all of the misrepresentations, the affidavit as corrected would show probable cause to arrest and prosecute Golino. This contention, which assumes that the omissions and misrepresentations were not material, hardly views the facts in the light most favorable to Golino as is required on a motion for summary judgment. Viewed in the light most favorable to Golino, the record indicates that appellants deliberately withheld, inter alia, the information that most of the eyewitnesses described the killer as thin, whereas Golino at the time weighed 215 pounds; that most of them described the killer as being clean shaven, whereas Golino at the time had a mustache; that the one eyewitness who said the killer had a mustache immediately positively identified a person other than Golino as the killer, and the man identified turned out to be Serra’s boyfriend; that Golino’s prime accuser, his former wife (whose extreme bias against Golino was confirmed at the 1984 state hearing), had made statements both inconsistent with those quoted in support of the warrant and recanting those quoted in support of the warrant; that the police had fingerprints which they strongly believed to have been left by the killer but which did not match the prints of Golino; and that the police knew the blood type of[*872] the killer but had declined to test Golino for blood type.

Plainly the information that was misrepresented or remained undisclosed in appellants’ presentations in support of probable cause were not immaterial to that question as a matter of law. Such matters as descriptions of the killer that did not fit Goli-no, an eyewitness’s identification of another plausible suspect as the culprit, the non-matching of fingerprints and blood types, are entirely relevant to the question of whether a person of reasonable caution would believe the murder had been committed by Golino. Possession of the undisclosed information at the 1984 state hearing might well have led the state court to rule that probable cause to prosecute Goli-no was lacking or at least to postpone any ruling on probable cause until after Golino had been tested for blood type. The latter course plainly would have led to a finding of no probable cause. The weight that a neutral magistrate would likely have given the above information, along with the other information that was concealed or misrepresented, is not a legal question but rather is a question to be resolved by the finder of fact.

Given, in addition, the evidence that appellants’ nondisclosure of the exculpatory information was deliberate, the district court properly concluded it could not rule as a matter of law that it was objectively reasonable for appellants to believe there was probable cause for the arrest and prosecution of Golino. Summary judgment was properly denied.

CONCLUSION

We have considered all of appellant' challenges to the decision of the district court and have found them to be without merit. The order denying summary judgment is affirmed.