Lopuhaä-Zwakenberg, Milan

The zeta Functions of Moduli Stacks of $G$-Zips and Moduli Stacks of Truncated Barsotti-Tate Groups

Doc. Math. 23, 1799-1828 (2018)
DOI: 10.25537/dm.2018v23.1799-1828
Communicated by Takeshi Saito

Summary

We study stacks of truncated Barsotti-Tate groups and the $G$-zips defined by Pink, Wedhorn & Ziegler. The latter occur naturally when studying truncated Barsotti-Tate groups of height $1$ with additional structure. By studying objects over finite fields and their automorphisms we determine the zeta functions of these stacks. These zeta functions can be expressed in terms of the Weyl group of the reductive group $G$ and its action on the root system. The main ingredients are the classification of $G$-zips over algebraically closed fields and their automorphism groups by Pink, Wedhorn & Ziegler, and the study of truncated Barsotti-Tate groups and their automorphism groups by Gabber & Vasiu.

Mathematics Subject Classification

11G10, 11G18, 14K10, 14L30

Keywords/Phrases

$G$-zips, Barsotti-Tate groups, moduli stacks, zeta functions

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Affiliation

Lopuhaä-Zwakenberg, Milan
Security Group, Technische Universiteit Eindhoven, Eindhoven, The Netherlands

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