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

Marc Masdeu; Marco Adamo Seveso

doi:10.1016/j.aim.2017.03.034

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

Marc Masdeu^*, Marco Adamo Seveso

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

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

Original language	English
Pages (from-to)	628-688
Number of pages	61
Journal	Advances in Mathematics
Volume	313
DOIs	https://doi.org/10.1016/j.aim.2017.03.034
Publication status	Published - 20 Jun 2017

Keywords

Chow motive
Dirac operator
Quaternionic modular forms

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10.1016/j.aim.2017.03.034

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title = "Dirac operators in tensor categories and the motive of quaternionic modular forms",

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, and provides the first motivic construction of new-subspaces of modular forms.",

keywords = "Chow motive, Dirac operator, Quaternionic modular forms",

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AU - Seveso, Marco Adamo

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N2 - 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–Livné. It also generalizes a construction of Scholl to indefinite division quaternion algebras, and provides the first motivic construction of new-subspaces of modular forms.

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

KW - Chow motive

KW - Dirac operator

KW - Quaternionic modular forms

UR - https://www.scopus.com/pages/publications/85018490163

U2 - 10.1016/j.aim.2017.03.034

DO - 10.1016/j.aim.2017.03.034

M3 - Article

AN - SCOPUS:85018490163

SN - 0001-8708

VL - 313

SP - 628

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

Keywords

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