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École normale supérieure de Paris |  |
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Transgressions of the Euler class and Eisenstein cohomology of GLN(Z)
Abstract : These notes were written to be distributed to the audience of the first author's Takagi lectures delivered June 23, 2018. These are based on a work-in-progress that is part of a collaborative project that also involves Akshay Venkatesh. In this work-in-progress we give a new construction of some Eisenstein classes for GL N (Z) that were first considered by Nori [41] and Sczech [44]. The starting point of this construction is a theorem of Sullivan on the vanishing of the Euler class of SL N (Z) vector bundles and the explicit transgression of this Euler class by Bismut and Cheeger. Their proof indeed produces a universal form that can be thought of as a kernel for a regularized theta lift for the reductive dual pair (GL N , GL 1). This suggests looking to reductive dual pairs (GL N , GL k) with k ≥ 1 for possible generalizations of the Eisenstein cocycle. This leads to fascinating lifts that relate the geometry/topology world of real arithmetic locally symmetric spaces to the arithmetic world of modular forms. In these notes we don't deal with the most general cases and put a lot of emphasis on various examples that are often classical.
Littérature citée [53 références]
https://hal-ens.archives-ouvertes.fr/hal-02886362
Contributeur : Marine Laffont <>
Soumis le : mercredi 1 juillet 2020 - 14:38:06
Dernière modification le : mercredi 2 juin 2021 - 16:26:59
Archivage à long terme le : : mercredi 23 septembre 2020 - 16:15:37
Contributeur : Marine Laffont <>
Soumis le : mercredi 1 juillet 2020 - 14:38:06
Dernière modification le : mercredi 2 juin 2021 - 16:26:59
Archivage à long terme le : : mercredi 23 septembre 2020 - 16:15:37
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