Le symbole de Hasse logarithmique

TL;DR

This paper introduces a logarithmic Hasse symbol within logarithmic ramification, explores its properties, and derives a logarithmic analogue of the principal ideal theorem, providing new insights into ramification theory.

Contribution

It defines the logarithmic Hasse symbol, studies its fundamental properties, and establishes a logarithmic version of the principal ideal theorem, extending classical ramification results.

Findings

Expression of the defect of the -adic Hasse principle

Logarithmic version of the principal ideal theorem

Properties of the logarithmic Hasse symbol

Abstract

In this article, we define the logarithmic Hasse symbol in the same way as the usual one but in the context of the logarithmic ramification. We study its fondamental properties. The interesting point is that we get an expression of the defect of the \^a-adic Hasse principle. Then we study particular cases and get a logarithmic version of the principal ideal theorem.