Work

Local Shtukas and Divisible Local Anderson Modules

Year: 2018

Type: article

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 theories of strict modules, which we review briefly.

Source: Canadian Journal of Mathematics

DOI: 10.4153/cjm-2018-016-2

Authors: Urs Hartl, Rajneesh Kumar Singh

Institutions: University of Münster, Ramakrishna Mission Vivekananda Educational and Research Institute

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Deutsche Forschungsgemeinschaft