Artin-Schreier-Witt lifts of purely inseparable extensions
摘要
For a discrete valued field K of positive characteristic, we analyze ramification in Artin-Schreier-Witt extensions and the existence of ferocious lifts of residue field extensions. Moreover, we prove that unlike the mixed characteristic case, arbitrarily large cyclic lifts of any finite purely inseparable modular extension exist and show how to explicitly construct them. More generally, we show that not only we can construct an arbitrary large degree Artin-Schreier-Witt lifts, but we can also construct the extension in such a way that the intermediate Artin-Schreier extensions are of any ramification type that is admissible by the residue. As a consequence, we get an affirmative answer to an open question of L. Xiao and I. Zhukov and show that there is no cap on the wild ramification index unlike the mixed characteristic case. We also show some interesting applications to p-algebras and construct cyclic lifts of other field extensions.