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The stack of G-zips is a Mori dream space

Part of: Linear algebraic groups and related topics Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  19 September 2025

Jean-Stefan Koskivirta
Jean-Stefan Koskivirta*
Affiliation:
University of Caen Normandie , Department of Mathematics, Caen 14032, France
*
e-mail: jeanstefan.koskivirta@gmail.com
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Abstract

We first extend previous results of Koskivirta with Wedhorn and Goldring regarding the existence of $\mu $-ordinary Hasse invariants for Hodge-type Shimura varieties to other automorphic line bundles. We also determine exactly which line bundles admit nonzero sections on the stack of G-zips of Pink–Wedhorn–Ziegler. Then, we define and study the Cox ring of the stack of G-zips and show that it is always finitely generated. Finally, beyond the case of line bundles, we define a ring of vector-valued automorphic forms on the stack of G-zips and study its properties. We prove that it is finitely generated in certain cases.

Keywords

Stack of G-zipsMori dream spaceautomorphic forms

MSC classification

Primary: 14G35: Modular and Shimura varieties 20G40: Linear algebraic groups over finite fields

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Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 36
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work was supported by JSPS KAKENHI Grant Number 21K13765 and by the University of Caen Normandie.

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