Endoscopic transfer of orbital integrals in large residual characteristic

TL;DR

This paper develops a motivic integration framework to transfer orbital integrals endoscopically in large residual characteristic, extending Waldspurger's transfer principles from characteristic zero.

Contribution

It constructs Shalika germs within motivic integration and establishes endoscopic transfer of smooth functions in large residual characteristic.

Findings

Constructed Shalika germs for orbital integrals

Established transfer of smooth functions in large residual characteristic

Extended Waldspurger's transfer principles to positive characteristic

Abstract

This article constructs Shalika germs in the context of motivic integration, both for ordinary orbital integrals and kappa-orbital integrals. Based on transfer principles in motivic integration and on Waldspurger's endoscopic transfer of smooth functions in characteristic zero, we deduce the endoscopic transfer of smooth functions in sufficiently large residual characteristic.