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

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.

preprint2014arXivOpen access
Alexandru GhitzaScott Mullane
math.AGmath.NT
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Alexandru GhitzaScott Mullane

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