Contents

Idea

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”.)

References

Reviews of the basic definition include

Definition 1 in

• Jared Weinstein, notes from lecture by Peter Scholze, Peter Scholze’s lectures on $p$-adic geometry, MSRI 2014 (pdf)

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

Last revised on September 5, 2014 at 11:30:48. See the history of this page for a list of all contributions to it.