Abstract
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].
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