Cohomological vanishing on Siegel modular varieties and applications to lifting Siegel modular forms
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2014
- DOI:
- 10.48550/arXiv.1403.2451
- arXiv:
- arXiv:1403.2451
- Bibcode:
- 2014arXiv1403.2451G
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Algebraic Geometry;
- 11F46;
- 11G18;
- 14G35
- E-Print:
- 18 pages