A Geometric Jacquet-Langlands Transfer for automorphic forms of higher weights

TL;DR

This paper presents a geometric method to transfer automorphic forms of higher weights via the study of mod p fibers of Shimura varieties and their cohomological correspondences, advancing understanding in automorphic representation theory.

Contribution

It introduces a geometric construction of the Jacquet-Langlands transfer for higher weight automorphic forms using the geometry of Shimura varieties and cohomological techniques.

Findings

Established a geometric framework for Jacquet-Langlands transfer

Analyzed the mod p fibers of Shimura varieties of Hodge type

Connected cohomological correspondences to automorphic form transfer

Abstract

In this paper, we give a geometric construction of the Jacquet-Langlands transfer for automorphic forms of higher weights by studying the geometry of the mod $p$ fibres of different Hodge type Shimura varieties which satisfy a mild assumption and the cohomological correspondences between them.