Algebraic Varieties, Birational Geometry and the Structure of the Galois Groups

代数簇、双有理几何和伽罗瓦群的结构

• 批准号: 1001662
• 负责人: Fedor Bogomolov
• 金额: $ 14.88万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1001662&HistoricalAwards=false
• 关键词: Algebraic; Varieties; Birational; Geometry; Structure

The project addresses the theory of universal spaces for birational invariants of algebraic varieties. One of the fundamental problems concerns the description of a natural class of quotients of products of projective spaces by the projective actions of abelian groups which held all finite birational invariants of varieties defined over algebraic closures of finite fields. The second more difficult problem which PI is going to address is to find a similar class of universal varieties for finite and then for infinite l-adic invariants of algebraic varieties defined over number fields.The Galois theory of functional fields provides with a series of results allowing to describe the cohomological birational invariants of algebraic varieties through the group cohomology. Thus this project addresses the problems at the interface of algebraic geometry, Galois theory and group theory.The PI is going to relate finite birational invariants of functional fields which are higher dimensional analogues of the nonramified Brauer group to the invariants of special systems of abelian subgroups in finite abelian groups.

该项目致力于代数簇的双有理不变量的泛空间理论。其中一个基本问题涉及到描述的自然类的concurent的产品的射影空间的投影行动的阿贝尔群举行所有有限双有理不变量的品种定义代数封闭的有限领域。第二个更困难的问题，其中PI是要解决的是找到一个类似的类的普遍品种有限，然后为无限的L-进不变量的代数簇定义的数字fields.The伽罗瓦理论的功能领域提供了一系列的结果，允许描述的上同调双有理不变量的代数簇通过组上同调。因此，这个项目解决的问题，在接口的代数几何，伽罗瓦理论和群论。PI将涉及有限双有理不变量的功能领域，这是高维类似的nonramified布劳尔群的不变量的特殊系统的阿贝尔子群在有限阿贝尔群。