A short review on local shtukas and divisible local Anderson modules

Hartl, Urs; Singh, Rajineesh Kumar

Abstract

We review the analog of crystalline Dieudonné theory for p-divisible groups in the arithmetic of function fields from [21]. In our theory, p-divisible groups are replaced by divisible local Anderson modules, and Dieudonné modules are replaced by local shtukas. We also explain their relation to global objects like Drinfeld modules and A-motives. We review the cohomology realizations of local shtukas and their comparison isomorphisms, and in the last section we explain how this yields the function field analog of Fontaine’s theory of p-adic Galois representations.