Towards explicit description of ramification filtration in the 2-dimensional case

Ramification of Higher Local Fields, Approaches and Questions

This is yet another attempt to organize facts, ideas and problems concerning ramification in finite extensions of complete discrete valuation fields with arbitrary residue fields. We start (§3) with a rather comprehensive description of classical ramification theory describing the behavior of ramification invariants in the case of perfect residue fields. This includes some observations that cou...

Towards Explicit Description of Ramification

The Ramification Groups and Different of a Compositum of Artin-Schreier Extensions

Let K be a function field over a perfect constant field of positive characteristic p, and L the compositum of n (degree p) Artin-Schreier extensions of K. Then much of the behavior of the degree pn extension L/K is determined by the behavior of the degree p intermediate extensions M/K. For example, we prove that a place of K totally ramifies/is inert/splits completely in L if and only if it tot...

On Ramification Theory in the Imperfect Residue Field Case

Let K be a complete discrete valuation field with the residue field K, charK = p > 0. If K is a perfect field, there exists a beautiful theory of ramification in algebraic extensions of K. Given a finite Galois extension L/K with the Galois group G, one can introduce a canonical filtration (Gi) in G with quite a natural behavior with respect to subextensions in L/K. Namely, if H is a normal sub...

On wild ramification in quaternion extensions par G . Griffith ELDER

This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain √ −1 (along with some partial results for the more general case). This catalog depends upon the refined ramification filtration, which as defined in [2] is associated with the biquadratic subfield. Mor...