Kato's Local epsilon conjecture: $l \neq p$ case

TL;DR

This paper proves the existence of specific elements in $p$-adic Iwasawa algebras related to local epsilon constants, confirming a conjecture by Kato and Fukaya in the case where $l eq p$.

Contribution

It establishes the existence of these elements in the $l eq p$ case, advancing the understanding of local epsilon conjectures in Iwasawa theory.

Findings

Existence of elements in $p$-adic Iwasawa algebras proved.

Confirmed Kato-Fukaya conjecture for $l eq p$ case.

Links between $p$-adic and $l$-adic epsilon constants clarified.

Abstract

Kato and Fukaya conjectured existence of certain elements in certain ($p$-adic) Iwasawa algebras which are related to Deligne-Langland's ($l$-adic) local epsilon constants. We prove the existence of these elements in the $l \neq p$ case.