# La conjecture $\epsilon$ locale de Kato en dimension $2$

## TL;DR

This paper proves a key functional equation for 2-dimensional p-adic Galois representations, completing Nakamura's proof of Kato's local epsilon-conjecture in dimension 2, advancing understanding in p-adic number theory.

## Contribution

It establishes an Iwasawa functional equation for 2-dimensional p-adic Galois representations, enabling the completion of Kato's epsilon-conjecture proof in this dimension.

## Key findings

- Proves an Iwasawa functional equation for 2-dimensional p-adic Galois representations.
- Completes Nakamura's proof of Kato's local epsilon-conjecture in dimension 2.
- Advances the understanding of p-adic Galois representations and epsilon-conjectures.

## Abstract

We show an Iwasawa functional equation for a two dimensional $p$-adic representation of the absolute Galois group of $\mathbf{Q}_p$. This allows us to complete Nakamura's proof of Kato's local $\epsilon$-conjecture in dimension $2$.