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

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].