{"title":"Compactifications of Iwahori-level Hilbert modular varieties","authors":"Fred Diamond","doi":"10.1016/j.jnt.2024.04.009","DOIUrl":null,"url":null,"abstract":"<div><p>We study minimal and toroidal compactifications of <em>p</em>-integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over <em>p</em>, 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 <em>q</em>-expansions of Hilbert modular forms, especially the effect of Hecke operators at primes over <em>p</em> over general base rings.</p></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"263 ","pages":"Pages 255-296"},"PeriodicalIF":0.6000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022314X24001161/pdfft?md5=b677fd9a2dc72751b9574178e03a6acc&pid=1-s2.0-S0022314X24001161-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001161","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
我们研究了希尔伯特模数变的 p 积分模型的极小和环压实。我们回顾了 p 以上素数岩堀级的理论，并将其扩展到某些更精细的级结构。我们还证明了最近关于岩堀级 Kodaira-Spencer 同构和退化映射的同调消失结果的紧凑化扩展。最后，我们将这一理论应用于研究希尔伯特模形式的 q-展开，特别是一般基环上 p 以上素数的赫克算子的影响。
期刊介绍：
The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.
The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.
Starting in May 2019, JNT will have a new format with 3 sections:
JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access.
JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions.
Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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