Griffiths-Schmid conditions for automorphic forms via characteristic p

2022/11/30 by Goldring, Wushi, Koskivirta, Jean-Stefan
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2211.16819

Abstract

We establish vanishing results for spaces of automorphic forms in characteristic 0 and characteristic p. We prove that for Hodge-type Shimura varieties, the weight of any nonzero automorphic form in characteristic 0 satisfies the Griffiths-Schmid conditions, by purely algebraic, characteristic p methods. We state a conjecture for general Hodge-type Shimura varieties regarding the vanishing of the space of automorphic forms in characteristic p in terms of the weight. We verify this conjecture for unitary PEL Shimura varieties of signature (n-1,1) at a split prime.

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