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

References in corpus (1)

• Geometric weight-shifting operators on Hilbert modular forms in characteristic p

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