Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory

Author:

Hwangk Yoon Sung,Jacob Bill

Abstract

AbstractLet F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 17 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Detecting fast solvability of equations via small powerful Galois groups;Transactions of the American Mathematical Society;2015-04-01

2. On graphs and valuations;Manuscripta Mathematica;2014-10-07

3. Small Galois groups that encode valuations;Acta Arithmetica;2012

4. Valuations and diameters of milnor K-rings;Israel Journal of Mathematics;2009-07

5. Compatible valuations and generalized Milnor -theory;Transactions of the American Mathematical Society;2007-04-24

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