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Higher Ramanujan equations and periods of abelian varieties

Abstract:

We describe higher dimensional generalizations of Ramanujan’s classical differential relations satisfied by the Eisenstein series E2, E4, E6. Such “higher Ramanujan equations” are given geometrically in terms of vector fields living on certain moduli stacks classifying abelian schemes equipped with suitable frames of their first de Rham cohomology. These vector fields are canonically constructed by means of the Gauss-Manin connection and the Kodaira-Spencer isomorphism. Using Mumford’s the...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1090/memo/1391

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
American Mathematical Society
Series:
Memoirs of the American Mathematical Society
Volume:
281
Issue:
1391
Publication date:
2022-01-03
Acceptance date:
2020-02-13
DOI:
EISSN:
1947–6221
ISSN:
0065-9266
EISBN:
978-1-4704-7324-2
ISBN:
978-1-4704-6019-8

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