Mathematical Sciences: Division Algebras Over Complete Fields & Over Function Fields of Curves

数学科学：完备域上的除法代数

• 批准号: 9401335
• 负责人: B Sethuraman
• 金额: $ 5.99万
• 依托单位: California State University-Northridge
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-06-15 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401335&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Division; Algebras; Over

Sethuraman This award supports work on three broad problems in the valuation theory of division algebras. The first problem is the study of non-tamely valued division algebras over complete fields of finite characteristic, and in particular, the study of the subfields of such algebras in terms of their valuation theory. The second problem is the study of division algebras defined over function fields of curves and the study of valuations on these algebras that are non-trivial on the field of constants. The principal investigator will also work on the classification of the Kummer subfields of tame division algebras over Henselian valued 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. ***

塞图拉曼 该奖项支持工作的三个广泛的问题，在估值理论的划分代数。 第一个问题是研究有限特征完备域上的非平凡值除代数，特别是研究这类代数的子域的赋值理论。 第二个问题是研究定义在曲线函数域上的除法代数，以及研究这些代数在常数域上的非平凡赋值。 首席研究员还将致力于分类的库默子域驯服司代数的Henselian值领域。 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。***