Cohomological vanishing on Siegel modular varieties and applications to lifting Siegel modular forms

2014/03/11 by Alexandru Ghitza, Ghitza, Alexandru, Scott Mullane +1
Mathematics · #11F46 #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1403.2451

openalex publication_date 2014/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use vanishing results for sheaf cohomology on Siegel modular varieties to study two lifting problems: (a) When can Siegel modular forms (mod p) be lifted to characteristic zero? This uses and extends previous results for cusp forms by Stroh and Lan-Suh. (b) When is the restriction of Siegel modular forms to the boundary of the moduli space a surjective map? We investigate this question in arbitrary characteristic, generalising analytic results of Weissauer and Arakawa.

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