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Dirac operators in tensor categories and the motive of quaternionic modular forms. (English) Zbl 1418.11065
Summary: 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.

MSC:
11F11 Holomorphic modular forms of integral weight
14F30 \(p\)-adic cohomology, crystalline cohomology
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