Equivariant epsilon conjecture for 1-dimensional Lubin-Tate groups

TL;DR

This paper formulates and proves a conjecture relating equivariant epsilon-constants and Galois cohomology for 1-dimensional Lubin-Tate groups over unramified extensions, extending previous ideas from multiplicative groups.

Contribution

It introduces a new conjecture linking epsilon-constants with Galois cohomology and proves it for unramified extensions when T is a Lubin-Tate group Tate module.

Findings

Conjecture proven for unramified extensions of degree prime to p.

Extension of ideas from multiplicative groups to Lubin-Tate groups.

Connects epsilon-constants with Galois cohomology in a new setting.

Abstract

In this paper we formulate a conjecture on the relationship between the equivariant \epsilon-constants (associated to a local p-adic representation V and a finite extension of local fields L/K) and local Galois cohomology groups of a Galois stable \mathbb{Z}_{p}-lattice T of V. We prove the conjecture for L/K being an unramified extension of degree prime to p and T being a p-adic Tate module of a one-dimensional Lubin-Tate group defined over \mathbb{Z}_{p} by extending the ideas of \cite{Breu} from the case of the multiplicative group \mathbb{G}_{m} to arbitrary one-dimensional Lubin-Tate groups. For the connection to the different formulations of the \epsilon-conjecture in \cite{BB}, \cite{FK}, \cite{Breu}, \cite{BlB} and \cite{BF} see \cite{Iz}.