Epsilon dichotomy for twisted linear models

Hang Xue and Pan Yan

Vol. 334 (2025), No. 1, 59–106

DOI: 10.2140/pjm.2025.334.59

Abstract

Let $E∕F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. We study a relation between the existence of twisted linear models on ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n(D)$ and the local root numbers.

Keywords

twisted linear models, epsilon dichotomy, relative trace formula

Mathematical Subject Classification

Primary: 11F70

Secondary: 22E50

Milestones

Received: 11 May 2024

Revised: 5 December 2024

Accepted: 8 December 2024

Published: 30 December 2024