Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo
# On the period conjecture of Gross-Deligne for fibrations

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Centre de conférences Marilyn et James Simons (IHES)
### Centre de conférences Marilyn et James Simons

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open.
In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication.The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.

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