This is a suit under -42 U.S.C. § 1983 against the Sheriff of Madison County, Indiana, complaining that by delaying the service of an arrest warrant for 20 months after it was issued by an Indiana state court the defendant made it more difficult for the plaintiff to put on an effective defense in the criminal prosecution growing out of the arrest, and in consequence the plaintiff was unjustly convicted. The district judge dismissed the suit on the authority of Heck v. Humphrey, 512 U.S. 477, 114 S.Ct. 2364, 129 L.Ed.2d 383 (1994). The dismissal was clearly correct, and the appeal sanctionably frivolous. Fed. R.App. P. 38. A convicted criminal who brings a civil rights suit that if successful would demonstrate the invalidity of his conviction must show that the conviction has been invalidated. Heck v. Humphrey, supra, 512 U.S. at 487, 114 S.Ct. at 2372; Anderson v. County of Montgomery, 111 F.3d 494, 498-99 (7th Cir.1997). McCurdy has not done this; in fact, he concedes the validity of the conviction and argues only that because he is not challenging the conviction and thus is not seeking to interfere with the criminal process his civil rights suit can proceed. The law is emphatically to the contrary. Ryan v. DuPage County Jury Comm’n, 105. F.3d 329 (7th Cir.1996) (per curiam).

A frivolous suit does not engage the jurisdiction of the federal courts. Hagans v. Lavine, 415 U.S. 528, 536-37, 94 S.Ct. 1372, 1378-79, 39 L.Ed.2d 577 (1974); Korzen v. Local Union, 75 F.3d 285, 289 (7th Cir.1996). Jurisdiction over the present suit may be doubly barred, because of the Eleventh Amendment. The suit was not against the individual sheriff who failed to serve the warrant in a timely fashion, but against , the “Sheriff of Madison County,” and if there were any doubt that this is an official-capacity suit it was dispelled at the oral argument of the appeal, when- the plaintiffs lawyer made clear that the suit would not abate if the sheriff were replaced, that instead it would continue against the new sheriff. Fed. R.App. P. 43(e)(1); Hafer v. Melo, 502 U.S. 21, 25, 112 S.Ct. 358, 361, 116 L.Ed.2d 301 (1991). An official-capacity suit is a suit against the office that the official who is named (or rather not “named”) as the defendant occupies. Id.; Kentucky v. Graham, 473 U.S. 159, 165-66, 105 S.Ct. 3099, 3104-05, 87 L.Ed.2d 114 (1985); Hernandez v. O’Malley, 98 F.3d 293, 297 (7th Cir.1996). So if that office is a part of state government, the suit against the officer is a suit against the state.

That alone would not bring down the bar of the Eleventh Amendment in this case, because a county or other local unit of government is not “the state” for purposes of that amendment. Mt. Healthy City School District v. Doyle, 429 U.S. 274, 280, 97 S.Ct. 568, 572, 50 L.Ed.2d 471 (1977); Hernandez v. O’Malley, supra, 98 F.3d at 297. Here, however, the sheriff was acting as the agent of the state court system, which is, of course, a part of the state for purposes of the Eleventh Amendment. The warrant was issued by a state court, and merely served by the sheriff. It could as well have been served by a bailiff or other court employee, for the sheriffs duty to serve the warrant was mandatory, Ind.Code §§ 36-2-13-5(a)(4), (5), so the county was not interposed as a decision-making body between the state and him. Lancaster v. Monroe County, 116 F.3d 1419, 1429-30 (11th Cir.1997). As an agent of the[*1146] state, though not an employee, the sheriffs office (the real defendant, remember) was a part of state government rather than county government when serving the state court’s warrant. So at least the cases hold, rejecting any contention that action by the state is limited to action by employees of the state. Ruehman v. Sheahan, 34 F.3d 525, 528 (7th Cir.1994); Scott v. O’Grady, 975 F.2d 366, 371 (7th Cir.1992); Pusey v. City of Youngstown, 11 F.3d 652, 657-58 (6th Cir.1993).

The added wrinkle here, however, is that by delaying the service of the arrest warrant for so long, the sheriffs office may have exceeded the scope of its delegated state authority, may have ceased, therefore, to be an arm of the state (much as if the sheriffs deputy had decided-to effect service by stuffing the warrant down McCurdy’s throat). If that is what happened here, this suit would probably be against the deputy in his personal capacity; but it would be (also or instead) against the sheriff in his official capacity if the deputy had been acting pursuant to a policy of the sheriff. Monell v. Department of Social Services, 436 U.S. 658, 694, 98 S.Ct. 2018, 2037, 56 L.Ed.2d 611 (1978). Conceivably, therefore, if improbably, the delay in serving the warrant on McCurdy was pursuant to official policy, and if so he would have an official-capacity suit that was not barred by the Eleventh Amendment. Ryan v. County of DuPage, 45 F.3d 1090, 1092 (7th Cir.1995); Ruehman v. Sheahan, supra, 34 F.3d at 528-30; McMillian v. Johnson, 88 F.3d 1573, 1582-83 (11th Cir.1996), aff'd. sub nom. McMillian v. Monroe County, — U.S. -, 117 S.Ct. 1734, 138 L.Ed.2d 1 (1997); Dotson v. Chester, 937 F.2d 920, 926-28 (4th Cir.1991). We need not explore this possibility (the possibility that the sheriff had a policy of delay in serving warrants), since the suit and appeal are in any event frivolous.

An order to show cause why the plaintiff or his attorney should not be sanctioned for filing a frivolous appeal will be issued.

Affirmed.