Transfer Principle for the Fundamental Lemma

TL;DR

This paper explains how the transfer principle enables the transfer of fundamental lemma identities across different p-adic fields, broadening the applicability of proven results from one field class to others.

Contribution

It demonstrates that the transfer principle can be used to extend the validity of fundamental lemma identities from one collection of fields to another, unifying their scope.

Findings

Fundamental lemma identities transfer across p-adic fields.

Transfer principle applies to identities of p-adic integrals.

Results hold for fields of both positive characteristic and characteristic zero.

Abstract

The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems about identities of p-adic integrals from one collection of fields to others. In particular, once the fundamental lemma has been established for one collection of fields (for example, fields of positive characteristic), it is also valid for others (fields of characteristic zero).