The local twisted Gan-Gross-Prasad conjecture for $\text{U}(V_K)/\text{U}(V)$

TL;DR

This paper proves the local twisted Gan-Gross-Prasad conjecture for certain unitary groups over nonarchimedean fields by establishing geometric expansions of trace formulas, advancing understanding in automorphic representation theory.

Contribution

It introduces geometric expansions of local trace formulas and proves the conjecture for tempered L-parameters in a new setting.

Findings

Proved the local twisted Gan-Gross-Prasad conjecture for U(V_K)/U(V).

Established geometric expansions of local trace formulas.

Applied results to nonarchimedean fields of odd residual characteristic.

Abstract

In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)/U(V)$ for tempered $L$-parameters over nonarchimedean fields of odd residual characteristic.