transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
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
David Goss, What is … a Shtuka?, Notices of the AMS 50(1), pp. 36-37.
Wikipedia, Drinfeld module – Shtuka
Definition 1 in
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.