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Thursday 28 Jan 2016p-adic deformation of motivic Chow groups

Andreas Langer - Exeter

H103 14:30-15:30

In their recent work on p-adic deformation of algebraic cycle classes

Bloch, Esnault and Kerz give an equivalent Hodge-theoretic condition

on the crystalline chern class when an algebraic cycle class lifts from char p

to a pro-class in the continous Chow-group of a formal lifting.

In my talk I will present a relative version of their work.

Starting with a projective smooth variety X defined over the ring R = n-truncated

Witt-vectors of a perfect field the classical Chow-group is replaced by a motivic

Chow-group which is defined using a mixed characteristic version of the Suslin-

Voevodsky complex and is still related to Milnor K- Cohomology.

I explain that the main results of Bloch-Esnault-Kerz formally hold in this relative

setting as well. One can give a Hodge-theoretic condition when an element in the

motivic Chow-group lifts to a pro-class on a formal lifting of X over W(R).

In the proof the relative de Rham-Witt complex and a relative version

of syntomic cohomology play a crucial role.


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