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arXiv · 2211.06922

Compactifications of Iwahori-level Hilbert modular varieties

Fred Diamond
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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.

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BibTeXRIS

Fred Diamond. 2022-11-13. Compactifications of Iwahori-level Hilbert modular varieties. https://doi.org/10.1016/j.jnt.2024.04.009

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