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-Livnè. It also generalizes a construction of Scholl to indefinite division quaternion algebras, and provides the first motivic construction of new-subspaces of modular forms.

Dirac operators in tensor categories and the motive of quaternionic modular forms / M. Masdeu, M.A. Seveso. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 313(2017 Jun), pp. 628-688. [10.1016/j.aim.2017.03.034]

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

M.A. Seveso
2017

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-Livnè. It also generalizes a construction of Scholl to indefinite division quaternion algebras, and provides the first motivic construction of new-subspaces of modular forms.
Chow motive; Dirac operator; Quaternionic modular forms; Mathematics (all)
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
giu-2017
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/558190
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