关于普通赫克轨道猜想

IF 0.9 1区 数学 Q2 MATHEMATICS
Pol van Hoften
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引用次数: 0

摘要

我们证明了霍奇型志村变的普通赫克轨道猜想。我们利用了柴氏的全局塞雷-塔特坐标以及达德兹奥关于等晶的单折线群的最新成果。本文的新内容是霍奇型志村变的赫克稳定子域的一般单旋转定理,以及普通赫克轨道的形式补全的刚性结果。在此过程中,我们证明了经典的塞雷-塔特坐标可以用单势形式群来描述,从而推广了豪的一个结果。
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 ordinary Hecke orbit conjecture

We prove the ordinary Hecke orbit conjecture for Shimura varieties of Hodge type at primes of good reduction. We make use of the global Serre–Tate coordinates of Chai as well as recent results of D’Addezio about the monodromy groups of isocrystals. The new ingredients in this paper are a general monodromy theorem for Hecke-stable subvarieties for Shimura varieties of Hodge type, and a rigidity result for the formal completions of ordinary Hecke orbits. Along the way, we show that classical Serre–Tate coordinates can be described using unipotent formal groups, generalising a result of Howe.

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来源期刊
CiteScore
1.80
自引率
7.70%
发文量
52
审稿时长
6-12 weeks
期刊介绍: ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.
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