Transfer to characteristic zero: appendix to "Fundamental Lemma of Jacquet-Rallis in positive characteristics" by Zhiwei Yun

TL;DR

This paper extends the proof of the Fundamental Lemma of Jacquet-Rallis from positive characteristic to characteristic zero, using transfer principles, for sufficiently large residue characteristics.

Contribution

It demonstrates that the Fundamental Lemma holds in characteristic zero by leveraging transfer principles, building on Yun's positive characteristic proof.

Findings

Fundamental lemma holds in characteristic zero for large residue characteristic.

Transfer principle effectively bridges positive characteristic and zero characteristic cases.

Supports broader applicability of the lemma in number theory and representation theory.

Abstract

This appendix shows that the Fundamental lemma of Jacquet-Rallis, proved by Zhiwei Yun in the positive charactersitic case, is also true in characteristic zero, when residue characteristic is sufficiently large. In fact, this follows immediately from the article "Transfer Principle for the Fundamental Lemma" by R. Cluckers, T.C. Hales and F.Loeser.