$p$一元变量的Hodge理论:综述

IF 0.7 4区数学 Q2 MATHEMATICS

Annales Polonici Mathematici Pub Date : 2020-05-01 DOI:10.4064/ap200516-31-8

Wiesalawa Niziol

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引用次数: 2

摘要

$p$-adic-Hodge理论是现代算术几何中最强大的工具之一。在这篇综述中，我们将回顾代数变体的$p$adic-Hodge理论，介绍分析变体的$p$adicHodge理论的最新发展，并讨论它在数论问题中的一些应用。这是2019年在克拉科夫举行的波兰数学学会成立100周年庆典上的演讲的延伸版本。

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Hodge theory of $p$-adic varieties: a survey

$p$-adic Hodge Theory is one of the most powerful tools in modern Arithmetic Geometry. In this survey, we will review $p$-adic Hodge Theory for algebraic varieties, present current developments in $p$-adic Hodge Theory for analytic varieties, and discuss some of its applications to problems in Number Theory. This is an extended version of a talk at the Jubilee Congress for the 100th anniversary of the Polish Mathematical Society, Krakow, 2019.

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来源期刊

Annales Polonici Mathematici 数学-数学

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： Annales Polonici Mathematici is a continuation of Annales de la Société Polonaise de Mathématique (vols. I–XXV) founded in 1921 by Stanisław Zaremba. The journal publishes papers in Mathematical Analysis and Geometry. Each volume appears in three issues.