Can a writ of habeas corpus be obtained by a prisoner in custody under a judgment of a state court?

Under AEDPA, a petition for a writ of habeas corpus by a prisoner in custody under a judgment of a state court may be granted only for violations of the Constitution or laws of the United States. 28 U.S.C. 2254(a); Williams v. Taylor, 529 U.S. at 375 n. 7 (2000). Federal habeas corpus relief is available for any claim decided on the merits in state court proceedings if the state court's adjudication of the claim:

28 U.S.C. 2254(d).

1. Contrary to or an Unreasonable Application of Federal Law