2017/07/06 by Vaidehee Thatte, Thatte, Vaidehee
Mathematics · #Algebraic Geometry and Number Theory #Rings, Modules, and Algebras #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.1707.01692
We previously obtained a generalization and refinement of results about the\nramification theory of Artin-Schreier extensions of discretely valued fields in\ncharacteristic p with perfect residue fields to the case of fields with more\ngeneral valuations and residue fields. As seen in VT16, the "defect" case gives\nrise to many interesting complications. In this paper, we present analogous\nresults for degree p extensions of arbitrary valuation rings in mixed\ncharacteristic (0,p) in a more general setting. More specifically, the only\nassumption here is that the base field K is henselian. In particular, these\nresults are true for defect extensions even if the rank of the valuation is\ngreater than 1. A similar method also works in equal characteristic,\ngeneralizing the results of VT16.\n