p-groups, p-rank, and semistable reduction of coverings of curves

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-02-06 DOI:10.2140/ant.2024.18.281

Yu Yang

引用次数: 0

Abstract

We prove various explicit formulas concerning $p$ -rank of $p$ -coverings of pointed semistable curves over discrete valuation rings. In particular, we obtain a full generalization of Raynaud’s formula for $p$ -rank of fibers over nonmarked smooth closed points in the case of arbitrary closed points. As an application, for abelian $p$ -coverings, we give an affirmative answer to an open problem concerning boundedness of $p$ -rank asked by Saïdi more than twenty years ago.

查看原文本刊更多论文

p 群、p 级和曲线覆盖的半可还原性

我们证明了关于离散估值环上尖的可半定曲线 p 覆盖的 p 级的各种显式公式。特别是，在任意闭点的情况下，我们得到了雷诺关于非标记光滑闭点上纤维 p 级公式的完全广义化。作为应用，对于无性 p 笼，我们给出了萨伊迪二十多年前提出的关于 p 级有界性的开放问题的肯定答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

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.