Mathematical Sciences: Brauer Groups and the Theory of Fields

数学科学：布劳尔群和场论

• 批准号: 9400650
• 负责人: David Saltman
• 金额: $ 22.11万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400650&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Brauer; Groups; Theory

Saltman This award supports research on both Brauer groups and the rationality problem for invariant fields. The principal investigator is specifically interested in the rationality problem for the center of the generic division algebra. A considerable part of this proposal concerns all these subjects, linked by the unramified cohomology. The principal investigator will determine if the unramified cohomology can be used to show the center of the generic division algebra is nonrational and if it can be used to show other invariant fields are nonrational. He will also see if the Merkuriev-Suslin theorem can be made more constructible and if the theory of toric varieties can be used to find good projective models for multiplicative invariant fields. The research supported is in the general area of field theory. Fields are algebraic structures similar to the rational numbers, the real numbers, and the complex numbers in that each nonzero element has an inverse with respect to multiplication. Field theory is a rich and deep subject with its historical roots arising from the early attempts to systematically describe the zeros of polynomials. ***

索特曼 该奖项支持研究两个布劳尔群体和合理性问题不变领域。 主要研究者特别感兴趣的是中心的合理性问题的一般司代数。 这个建议的相当一部分涉及所有这些主题，由unramified上同调。 主要研究者将确定非分歧上同调是否可以用来表明一般除代数的中心是非有理数的，以及它是否可以用来表明其他不变域是非有理数的。 他还将看到，如果Merkuriev-Suslin定理可以更加建设性，如果理论的复曲面品种可以用来找到良好的投影模型乘法不变领域。 支持的研究是在场论的一般领域。 域是类似于有理数、真实的数和复数的代数结构，因为每个非零元素都有关于乘法的逆。 场论是一门内容丰富而深刻的学科，其历史根源来自于系统地描述多项式零点的早期尝试。***