On 𝑝-adic 𝐿-functions for Hilbert modular forms

IF 2 4区数学 Q1 MATHEMATICS Memoirs of the American Mathematical Society Pub Date : 2024-06-01 DOI:10.1090/memo/1489

John Bergdall, David Hansen

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.

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论希尔伯特模态的𝑝-adic𝐿-函数

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.

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