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

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	628-688
Nombre de pàgines	61
Revista	Advances in Mathematics
Volum	313
DOIs	https://doi.org/10.1016/j.aim.2017.03.034
Estat de la publicació	Publicada - 20 de juny 2017

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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",

author = "Marc Masdeu and Seveso, \{Marco Adamo\}",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = jun,

day = "20",

doi = "10.1016/j.aim.2017.03.034",

language = "English",

volume = "313",

pages = "628--688",

journal = "Advances in Mathematics",

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T1 - Dirac operators in tensor categories and the motive of quaternionic modular forms

AU - Masdeu, Marc

AU - Seveso, Marco Adamo

PY - 2017/6/20

Y1 - 2017/6/20

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

EP - 688

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

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