A generalisation of the Abhyankar Jung theorem to associated graded rings of valuations

Author:

CUTKOSKY STEVEN DALE

Abstract

AbstractSuppose thatRSis an extension of local domains andν* is a valuation dominatingS. We consider the natural extension of associated graded rings along the valuation grν*(R) → grν*(S). We give examples showing that in general, this extension does not share good properties of the extensionRS, but after enough blow ups above the valuations, good properties of the extensionRSare reflected in the extension of associated graded rings. Stable properties of this extension (after blowing up) are much better in characteristic zero than in positive characteristic. Our main result is a generalisation of the Abhyankar–Jung theorem which holds for extensions of associated graded rings along the valuation, after enough blowing up.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference28 articles.

1. Commutative Algebra

2. O. Zariski Le problème des modules pour les branches planes. Course given at the Centre de Mathématiques de l'École Polytechnique, Paris, 1973, with an appendix by Bernard Teissier, Second Edition (Hermann, Paris, 1983).

3. Equimultiplicity, algebraic elimination, and blowing-up

4. Valuations in Function Fields of Surfaces

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3