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On log differentials of local fields

Nicola Mazzari

Abstract

We prove a logarithmic version of Fontaine's classic result on differentials of $\mathcal{O}_{\bar K}$ over $\mathcal{O}_K$.

On log differentials of local fields

Abstract

We prove a logarithmic version of Fontaine's classic result on differentials of over .

Paper Structure

This paper contains 4 sections, 1 theorem, 18 equations.

Table of Contents

  1. Introduction
  2. Logarithmic differentials
  3. The log structure on $\mathcal{O}_{\bar{K}}$
  4. The map $\mathop{\mathrm{dlog}}\nolimits$

Key Result

Theorem 1.1

There is a natural surjection compatible with $\mathop{\mathrm{dlog}}\nolimits_F$. Moreover it induces an isomorphism

Theorems & Definitions (3)

  • Theorem 1.1
  • proof : Proof of the Theorem
  • Remark 2.1