一般$p$进域上的算术基本引理猜想

IF 2.5 1区 数学 Q1 MATHEMATICS
A. Mihatsch, W. Zhang
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引用次数: 5

摘要

在具有奇残基基数$q\geq \dim V$的一般$p$ -进域上证明了算术基本引理猜想。我们的策略类似于第二个作者在$\mathbb{Q}\_p$上证明AFL时使用的策略,但只需要在Shimura变量上的除数生成级数的模块化(而不是其积分模型)。由此带来的灵活性的增加使我们能够在任意基域上工作。为了实施我们的策略,我们还将Howard(2012)关于CM循环相交的结果和Ehlen-Sankaran(2018)关于Green函数比较的结果从$\mathbb{Q}$推广到一般的全实基场。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field
We prove the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field with odd residue cardinality $q\geq \dim V$. Our strategy is similar to the one used by the second author in his proof of the AFL over $\mathbb{Q}\_p$, but only requires the modularity of divisor generating series on the Shimura variety (as opposed to its integral model). The resulting increase in flexibility allows us to work over an arbitrary base field. To carry out our strategy, we also generalize results of Howard (2012) on CM cycle intersection and of Ehlen–Sankaran (2018) on Green function comparison from $\mathbb{Q}$ to general totally real base fields.
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来源期刊
CiteScore
4.50
自引率
0.00%
发文量
103
审稿时长
6-12 weeks
期刊介绍: The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS. The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards. Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004. The Journal of the European Mathematical Society is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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