

Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
December 16, 2014 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)






Periods of connections and a conjecture of Gross–Deligne
Javier Fresan^{} 
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Abstract:
Motivated by a new approach to the
ChowlaSelberg formula, Gross and Deligne conjectured at the end of
the 70s that periods of geometric Hodge structures with
multiplication by an abelian number field are products of special
values of the gamma function, with exponents determined by the Hodge
decomposition. I will explain a proof of an alternating variant of
this conjecture for the cohomology groups of smooth, projective
varieties with an automorphism of finite order. The main ingredient
is a globaltolocal formula for periods of flat vector bundles due
to Saito and Terasoma.

