Geodesic
The zeta Functions of Moduli Stacks of $G$-Zips and Moduli Stacks of Truncated Barsotti-Tate Groups
Documenta mathematica, Tome 23 (2018), pp. 1799-1828
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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.
DOI : 10.4171/dm/660
Classification : 11G10, 11G18, 14K10, 14L30
Mots-clés : zeta functions, G-zips, Barsotti-Tate groups, moduli stacks 
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     author = {Milan Lopuha\"a-Zwakenberg},
     title = {The zeta {Functions} of {Moduli} {Stacks} of $G${-Zips} and {Moduli} {Stacks} of {Truncated} {Barsotti-Tate} {Groups}},
     journal = {Documenta mathematica},
     pages = {1799--1828},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/660},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/660/}
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Milan Lopuhaä-Zwakenberg. The zeta Functions of Moduli Stacks of $G$-Zips and Moduli Stacks of Truncated Barsotti-Tate Groups. Documenta mathematica, Tome 23 (2018), pp. 1799-1828. doi: 10.4171/dm/660

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