Ramification theory for degree p extensions of arbitrary valuation rings in mixed characteristic (0, p)

JOURNAL OF ALGEBRA

卷:507

Article

Thatte, Vaidehee¹ 

[1] Queens Univ, Dept Math & Stat, 48 Univ Ave, Kingston, ON K7L 3N6, Canada

关键词: Ramification theory;    Valuation rings;    Defect;    Mixed characteristic;    Swan conductor;    Refined Swan conductor;   

DOI  :  10.1016/j.jalgebra.2018.04.016

来源: Elsevier

【 摘 要 】

We previously obtained a generalization and refinement of results about the ramification theory of Artin Schreier extensions of discretely valued fields in characteristic p with perfect residue fields to the case of fields with more general valuations and residue fields. As seen in [5], the defect case gives rise to many interesting complications. In this paper, we present analogous results for degree p extensions of arbitrary valuation rings in mixed characteristic (0,p) in a more general setting. More specifically, the only assumption here is that the base field K is henselian. In particular, these results are true for defect extensions even if the rank of the valuation is greater than 1. A similar method also works in equal characteristic, generalizing the results of [5]. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free