In arithmetic geometry over a finite field a shtuka on an arithmetic scheme is essentially an equivariant algebraic vector bundle on the product of the scheme with a given arithmetic curve, where equivariance is with respect to the action of the Frobenius endomorphism (e.g. Scholze-Weinstein, def. 1).

( Shtuka is a Russian word colloquially meaning “thing”.)


Reviews of the basic definition include

Definition 1 in

More conceptual discussion, in the context of the function field analogy, is in

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