Bases of associated Galois modules in general wildly ramified extensions and in elementary abelian extensions of degree $p^2$

Paper

Abstract

For a wildly ramified extension

of complete discrete valuation fields we study collections of elements of

(where

) that fit well for constructing bases of various associated Galois modules and orders. In the case

(where

is the characteristic of residue fields) we are able to compute the action of the elements

on the valuation filtration; here

are generators of

. If the ramification jumps of

are distinct modulo

then these elements do yield "good enough" bases in question.