Indices of inseparability and refined ramification breaks

TL;DR

This paper investigates the relationship between indices of inseparability and refined ramification breaks in certain p-adic field extensions, providing a formula connecting these invariants under specific conditions.

Contribution

It establishes a formula linking the refined ramification break to the index of inseparability for totally ramified (Z/pZ)^2-extensions when p>2.

Findings

Derived a formula for b_* in terms of i_1 and b

Identified conditions under which the formula holds

Enhanced understanding of ramification invariants in local field extensions

Abstract

Let K be a finite extension of Q_p and let L/K be a totally ramified (Z/pZ)^2-extension which has a single ramification break b. Byott and Elder defined a "refined ramification break" b_* for L/K. In this paper we prove that if p>2 and the index of inseparability i_1 of L/K is not equal to p^2b-pb then b_*=i_1-p^2b+pb+b.