Geodesic
$p$-Adic Deformation of Motivic Chow Groups
Documenta mathematica, Tome 23 (2018), pp. 1863-1894.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

For a smooth projective scheme $Y$ over $W(k)$ we consider an element in the motivic Chow group of the reduction $Y_{m}$ over the truncated Witt ring $W_{m}(k)$ 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 $Y_\bullet$. The result extends previous work of Bloch-Esnault-Kerz 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 $Y_{m}$ over the ind-scheme ${Spec}\,W_{\bullet}(W_{m}(k))$.
Classification : 14F30, 14F40, 19E15
Keywords: $p$-adic arithmetic geometry, relative de Rham-Witt complex, syntomic complex, motivic Chow groups 
@article{DOCMA_2018__23__a10,
     author = {Langer, Andreas},
     title = {$p${-Adic} {Deformation} of {Motivic} {Chow} {Groups}},
     journal = {Documenta mathematica},
     pages = {1863--1894},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a10/}
}
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Langer, Andreas. $p$-Adic Deformation of Motivic Chow Groups. Documenta mathematica, Tome 23 (2018), pp. 1863-1894. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a10/