1 results
Local Shtukas and Divisible Local Anderson Modules
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 71 / Issue 5 / October 2019
- Published online by Cambridge University Press:
- 12 March 2019, pp. 1163-1207
- Print publication:
- October 2019
-
- Article
-
- You have access
- Open access
- Export citation
-
We develop the analog of crystalline Dieudonné theory for
$p$-divisible groups in the arithmetic of function fields. In our theory 
$p$-divisible groups are replaced by divisible local Anderson modules, and Dieudonné modules are replaced by local shtukas. We show that the categories of divisible local Anderson modules and of effective local shtukas are anti-equivalent over arbitrary base schemes. We also clarify their relation with formal Lie groups and with global objects like Drinfeld modules, Anderson’s abelian 
$t$-modules and 
$t$-motives, and Drinfeld shtukas. Moreover, we discuss the existence of a Verschiebung map and apply it to deformations of local shtukas and divisible local Anderson modules. As a tool we use Faltings’s and Abrashkin’s theories of strict modules, which we review briefly.
