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arXiv · 2211.16817

Divisibility of mod $p$ automorphic forms and the cone conjecture for certain Shimura varieties of Hodge-type

Wushi Goldring·Jean-Stefan Koskivirta
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Abstract

For several Hodge-type Shimura varieties of good reduction in characteristic $p$, we show that the cone of weights of automorphic forms is encoded by the stack of $G$-zips of Pink-Wedhorn-Ziegler. This establishes several instances of a general conjecture formulated in previous papers by the authors. Furthermore, we prove in these cases that any mod $p$ automorphic form whose weight lies in a specific region of the weight space is divisible by a partial Hasse invariant. This generalizes to other Shimura varieties previous results of Diamond--Kassaei on Hilbert modular forms.

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Wushi Goldring, Jean-Stefan Koskivirta. 2022-11-30. Divisibility of mod $p$ automorphic forms and the cone conjecture for certain Shimura varieties of Hodge-type. https://arxiv.org/abs/2211.16817

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