Dirac operators in tensor categories and the motive of quaternionic modular forms

TL;DR

This paper constructs a motive associated with quaternionic modular forms of any weight, extending previous work to odd weights and indefinite division quaternion algebras, enriching the understanding of motives in this context.

Contribution

It introduces a new motive framework for quaternionic modular forms of arbitrary weight, generalizing prior constructions to include odd weights and indefinite division quaternion algebras.

Findings

Construction of a motive for modular forms on indefinite division quaternion algebras.

Extension of previous work to odd weights in the context of quaternionic modular forms.

Generalization of Scholl's construction to indefinite division quaternion algebras.

Abstract

We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livn\'e. It also generalizes a construction of Scholl to indefinite division quaternion algebras.