不完全域上代数变量的不变量

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2019-03-25 DOI:10.2748/tmj.20200611

Hiromu Tanaka

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引用次数: 13

摘要

我们引入了不完全域上代数变量的四个不变量，每个不变量都度量几何非正态性或几何非约性。本文的第一个目标是建立这些不变量的基本性质。然后我们将我们的结果应用到不完美领域的曲线上。特别地，我们建立了一个格变化公式，证明了格为1的非光滑规则曲线的有界性。我们还计算了一些显式例子的不变量。

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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Invariants of algebraic varieties over imperfect fields

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of these invariants. We then apply our results to curves over imperfect fields. In particular, we establish a genus change formula and prove the boundedness of non-smooth regular curves of genus one. We also compute our invariants for some explicit examples.

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