Compactifications of Iwahori-level Hilbert modular varieties

Fred Diamond

doi:10.1016/j.jnt.2024.04.009

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.

Original language	English
Journal	Journal of Number Theory
Volume	263
DOIs	https://doi.org/10.1016/j.jnt.2024.04.009
Publication status	Published - 17 May 2024

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title = "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.",

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AU - Diamond, Fred

PY - 2024/5/17

Y1 - 2024/5/17

N2 - 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.

AB - 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.

U2 - 10.1016/j.jnt.2024.04.009

DO - 10.1016/j.jnt.2024.04.009

M3 - Article

SN - 0022-314X

VL - 263

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Compactifications of Iwahori-level Hilbert modular varieties

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