A Local Trace Formula for the Local Gan-Gross-Prasad Conjecture for Special Orthogonal Groups

TL;DR

This paper proves the tempered part of the local Gan-Gross-Prasad conjecture for special orthogonal groups over local fields of characteristic zero, extending Waldspurger's results to all such fields by combining previous work.

Contribution

It introduces a local trace formula approach that generalizes Waldspurger's proof from p-adic fields to all local fields of characteristic zero.

Findings

Proof of the tempered local Gan-Gross-Prasad conjecture for special orthogonal groups over any local field of characteristic zero.

Extension of Waldspurger's p-adic results to a broader class of local fields.

Development of a local trace formula method for this conjecture.

Abstract

Through combining the work of Jean-Loup Waldspurger (\cite{waldspurger10} and \cite{waldspurgertemperedggp}) and Rapha\"el Beuzart-Plessis (\cite{beuzart2015local}), we give a proof for the tempered part of the local Gan-Gross-Prasad conjecture (\cite{ggporiginal}) for special orthogonal groups over any local fields of characteristic zero, which was already proved by Waldspurger over $p$-adic fields.