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Isaac Newton Institute for Mathematical Sciences

On cristalline Deligne cohomology

1st September 2006

Author: Vologodsky, V (Chicago )

Abstract

Let X be a smooth projective variety and Y be its infinitesimal deformation. I will give a complete answer to the following question:

when a class in the algebraic K-group of $X$ lifts to $Y$?

The answer will be given in terms of the infinitesimal variation of Hodge structure associated to Y.