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arXiv · 2111.10160

Kodaira-Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace

Fred Diamond
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Abstract

We consider integral models of Hilbert modular varieties with Iwahori level structure at primes over p, first proving a Kodaira-Spencer isomorphism that gives a concise description of their dualizing sheaves. We then analyze fibres of the degeneracy maps to Hilbert modular varieties of level prime to p and deduce the vanishing of higher direct images of structure and dualizing sheaves, generalizing prior work with Kassaei and Sasaki (for p unramified in the totally real field F). We apply the vanishing results to prove flatness of the finite morphisms in the resulting Stein factorizations, and combine them with the Kodaira-Spencer isomorphism to simplify and generalize the construction of Hecke operators at primes over p on Hilbert modular forms (integrally and mod p).

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BibTeXRIS

Fred Diamond. 2021-11-19. Kodaira-Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace. https://doi.org/10.1017/fms.2025.13

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