Thursday 28 Jan 2016: p-adic deformation of motivic Chow groups
Andreas Langer - Exeter
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.