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arXiv · 1511.03697

Local Shtukas and Divisible Local Anderson Modules

Urs Hartl·Rajneesh Kumar Singh
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Abstract

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 theory of strict modules, which we review to some extent.

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Urs Hartl, Rajneesh Kumar Singh. 2019-01-21. Local Shtukas and Divisible Local Anderson Modules. https://doi.org/10.4153/cjm-2018-016-2

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