{"title":"On 𝑝-adic 𝐿-functions for Hilbert modular forms","authors":"John Bergdall, David Hansen","doi":"10.1090/memo/1489","DOIUrl":null,"url":null,"abstract":"We construct \n\n \n p\n p\n \n\n-adic \n\n \n L\n L\n \n\n-functions associated with \n\n \n p\n p\n \n\n-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in \n\n \n p\n p\n \n\n-adic families, and does not require any small slope or non-criticality assumptions on the \n\n \n p\n p\n \n\n-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group, and a smoothness theorem for certain eigenvarieties at critically refined points.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":"77 14","pages":""},"PeriodicalIF":4.7000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/memo/1489","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
Abstract
We construct
p
p
-adic
L
L
-functions associated with
p
p
-refined cohomological cuspidal Hilbert modular forms over any totally real field under a mild hypothesis. Our construction is canonical, varies naturally in
p
p
-adic families, and does not require any small slope or non-criticality assumptions on the
p
p
-refinement. The main new ingredients are an adelic definition of a canonical map from overconvergent cohomology to a space of locally analytic distributions on the relevant Galois group, and a smoothness theorem for certain eigenvarieties at critically refined points.
在一个温和的假设条件下，我们构建了与任何全实数域上 p p 精化同调尖顶希尔伯特模形式相关的 p p -adic L L 函数。我们的构造是典型的，在 p p -adic 族中自然变化，并且不需要任何小斜率或 p p - 精化的非临界假设。主要的新成分是一个从过敛同调到相关伽罗瓦群上局部解析分布空间的规范映射的自洽定义，以及在临界细化点上某些特征变量的平滑性定理。
期刊介绍：
ACS Applied Bio Materials is an interdisciplinary journal publishing original research covering all aspects of biomaterials and biointerfaces including and beyond the traditional biosensing, biomedical and therapeutic applications.
The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrates knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important bio applications. The journal is specifically interested in work that addresses the relationship between structure and function and assesses the stability and degradation of materials under relevant environmental and biological conditions.
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