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

该奖项支持在除法代数估值理论中的三个广泛问题上的工作。第一个问题是研究有限特征完全域上的非定值除法代数，特别是研究这类代数的子域的定值理论。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。首席研究员还将对Henselian值域上的驯服划分代数的Kummer子域进行分类。支持的研究是在一般领域的场论。域是类似于有理数、实数和复数的代数结构，因为每个非零元素相对于乘法有一个逆。场论是一门丰富而深刻的学科，其历史根源源于早期系统地描述多项式零点的尝试。＊＊＊

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. ***