Compactifications of Iwahori-level Hilbert modular varieties

Abstract

We study minimal and toroidal compactifications of $p$-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over $p$, and extend it to certain finer level structures. We also prove extensions to compactifications of recent results on Iwahori-level Kodaira--Spencer isomorphisms and cohomological vanishing for degeneracy maps. Finally we apply the theory to study $q$-expansions of Hilbert modular forms, especially the effect of Hecke operators at primes over $p$ over general base rings.

34 pages, minor corrections to v1

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• A Serre weight conjecture for geometric Hilbert modular forms in characteristic p
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• Hecke operators and the coherent cohomology of Shimura varieties
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Cited by in corpus (2)

• Eigenvariety for partially classical Hilbert modular forms
• Kodaira-Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace