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In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of complex multiplication theory. A shtuka (also called F-sheaf or chtouca) is a sort of ...
Spelled chtouca in the French literature, a mathematical shtuka is, roughly speaking, a special kind of module with a Frobenius-linear endomor-phism (as explained below) attached to a curve over. a finite field. Shtukas came from a fundamental analogy between differentiation and the p-th power mapping in prime characteristic p.
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Drinfeld shtukas. The moduli space of elliptic curves only associates Galois representations to automorphic forms for GL2 =Q satisfying a certain condition at Q1 = R (namely, to modular forms). The moduli space of elliptic sheaves has a similar restriction at 1, and this corresponds to restricting ji to be modi cations at 1.
Abstract. We provide explicit equations for moduli spaces of Drinfeld shtukas over the projective line with Γ(N), Γ1(N) and Γ0(N) level structures, where N is an effective divisor on P1. If the degree of N is high enough, these moduli spaces are relative surfaces.
15 de jun. de 2021 · p-adic shtukas and the theory of global and local Shimura varieties. Georgios Pappas, Michael Rapoport. We establish basic results on p-adic shtukas and apply them to the theory of local and global Shimura varieties, and on their interrelation. We construct canonical integral models for (local, and global) Shimura varieties of Hodge type with ...
A mixed characteristic shtuka will replace the smooth curve Xwith X= SpecZ, and the closed point xwill be given by a prime number p. Then Xb= Spf Z p. We would like to define local shtukas by making these substitutions everywhere in Definition 2.2. However, we immediately run into the problem that there is no suitable analog of S× Fp Xb. There is
a shtuka is a vector bundle with some additional marked local structure. We nally introduce some ideas from the theory of algebraic stacks, with an eye towards the construction of moduli spaces of vector bundles and shtukas. The key point is to represent spaces using functors de ned only on perfectoid spaces
