18 U.S.C. §1621. Perjury generally  (United States Code)

Whoever--

(1) having taken an oath before a competent tribunal, officer, or person, in any case in which a law of the United States authorizes an oath to be administered, that he will testify, declare, depose, or certify truly, or that any written testimony, declaration, deposition, or certificate by him subscribed, is true, willfully and contrary to such oath states or subscribes any material matter which he does not believe to be true; or

(2) in any declaration, certificate, verification, or statement under penalty of perjury as permitted under section 1746 of title 28, United States Code, willfully subscribes as true any material matter which he does not believe to be true;

is guilty of perjury and shall, except as otherwise expressly provided by law, be fined under this title or imprisoned not more than five years, or both. This section is applicable whether the statement or subscription is made within or without the United States.

From Model Criminal Jury Instructions for the Eighth Circuit Federal Courts

The crime of perjury, as charged in [Count __of] the indictment, has five essential elements, which are:

One, the defendant testified under [oath] [affirmation] (describe proceeding, e.g., at the trial of Smith v. Jones) that (insert alleged false testimony);

Two, the testimony so given was false;

Three, at the time he testified, the defendant knew such testimony was false;

Four, the defendant voluntarily and intentionally gave such testimony; and

Five, the false testimony was material.

False testimony is "material" if the testimony is capable of influencing (insert name of tribunal, etc.) on the issue before it.

(Insert paragraph describing Government's burden of proof; see Instruction 3.09. supra.)

(Committee Comments and Notes omitted)