p-adic deformation of motivic Chow groups
Langer, A
Date: 18 December 2018
Journal
Documenta Mathematica
Publisher
Deutsche Mathematiker
Publisher DOI
Abstract
For a smooth projective scheme Y over W(k) we consider
an element in the motivic Chow group of the reduction Ym over
the truncated Witt ring Wm(k) and give a “Hodge” criterion - using
the crystalline cycle class in relative crystalline cohomology - for the
element to lift to the continuous Chow group of the associated p-adic
formal ...
For a smooth projective scheme Y over W(k) we consider
an element in the motivic Chow group of the reduction Ym over
the truncated Witt ring Wm(k) and give a “Hodge” criterion - using
the crystalline cycle class in relative crystalline cohomology - for the
element to lift to the continuous Chow group of the associated p-adic
formal scheme Y•. The result extends previous work of Bloch-EsnaultKerz
on the p-adic variational Hodge conjecture to a relative setting.
In the course of the proof we derive two new results on the relative de
Rham-Witt complex and its Nygaard filtration, and work with a relative
version of syntomic complexes to define relative motivic complexes
for a smooth lifting of Ym over the ind-scheme Spec W•(Wm(k)).
Mathematics and Statistics
Faculty of Environment, Science and Economy
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