Recent Developments in Positive Characteristic Methods in Commutative Algebra: Frobenius Operators and Cartier Algebras

交换代数正特征方法的最新进展：Frobenius 算子和 Cartier 代数

• 批准号: 1507908
• 负责人: Yongwei Yao
• 金额: $ 2.45万
• 依托单位: Georgia State University Research Foundation, Inc.
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-02-15 至 2016-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1507908&HistoricalAwards=false
• 关键词: Recent; Developments; Positive; Characteristic; Methods

This award supports participation in the conference Recent Developments in Positive Characteristic Methods in Commutative Algebra, held during March 13-15, 2015, at Georgia State University, Atlanta, Georgia. The motivation behind the conference is to bring together researchers, including postdoctoral researchers and graduate students, in commutative algebra and related areas, in order to exchange ideas and discuss recent developments in positive characteristic methods. Top researchers in the field as well as postdocs and graduate students will be invited to speak at the conference. To make the conference accessible to all participants, introductory talks are scheduled. The conference will provide a platform for the participants to start exploring research aspects related to the highlighted topics, and it is anticipated that they will contribute research progress in these areas within a few years. More information can be found on the conference web site: http://www2.gsu.edu/~matfxe/gsu-usc/foca.htmlThe conference will focus on recent developments in positive characteristic methods. Research on positive characteristic methods has seen tremendous developments in recent years via using concepts related to the Frobenius homomorphisms. This includes the tight closure theory in characteristic p, singularities derived via tight closure theory, as well as the corresponding singularities in characteristic zero (via reduction to characteristic p) in algebraic geometry. The highlights of the conference, Frobenius operators and Cartier algebras, also involve the Frobenius homomorphisms in very fundamental ways. Both of them have intricate connections with the tight closure theory, birational geometry, F-modules, F-stability, test ideals, jumping numbers, anti-canonical covers, etcetera. Very recent research also includes the invariant "Frobenius complexity" being defined in order to measure whether a ring Frobenius operators is finitely generated. This conference will provide an opportunity for the participants to get exposed to the topics, exchange ideas, forge collaborations, and contribute to these research areas.

该奖项支持参加 2015 年 3 月 13 日至 15 日在佐治亚州亚特兰大市佐治亚州立大学举行的交换代数正特征方法的最新发展会议。会议的目的是将交换代数及相关领域的研究人员（包括博士后研究人员和研究生）聚集在一起，交流思想并讨论正特征方法的最新发展。该领域的顶尖研究人员以及博士后和研究生将被邀请在会议上发言。为了使所有与会者都能参加会议，安排了介绍性演讲。会议将为与会者提供一个开始探索与重点主题相关的研究方面的平台，预计他们将在几年内为这些领域的研究进展做出贡献。 更多信息可以在会议网站上找到：http://www2.gsu.edu/~matfxe/gsu-usc/foca.html 会议将重点关注积极特征方法的最新发展。近年来，通过使用与 Frobenius 同态相关的概念，正特征方法的研究取得了巨大的发展。这包括特征 p 中的紧闭理论、通过紧闭理论导出的奇点以及代数几何中特征零（通过简化为特征 p）中的相应奇点。会议的亮点是弗罗贝尼乌斯算子和卡地亚代数，也涉及非常基本的弗罗贝尼乌斯同态。它们都与紧闭包理论、双有理几何、F 模、F 稳定性、测试理想、跳跃数、反规范覆盖等有着复杂的联系。最近的研究还包括定义不变的“弗罗贝尼乌斯复杂度”，以衡量环弗罗贝尼乌斯算子是否是有限生成的。这次会议将为与会者提供一个接触主题、交流想法、建立合作并为这些研究领域做出贡献的机会。