Geodesic
$p$-Adic Deformation of Motivic Chow Groups
Documenta mathematica, Tome 23 (2018), pp. 1863-1894
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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–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 Ym​ over the ind-scheme SpecW∙​(Wm​(k)).
DOI : 10.4171/dm/662
Classification : 14F30, 14F40, 19E15
Mots-clés : p-adic arithmetic geometry, relative de Rham-Witt complex, syntomic complex, motivic Chow groups 
@article{10_4171_dm_662,
     author = {Andreas Langer},
     title = {$p${-Adic} {Deformation} of {Motivic} {Chow} {Groups}},
     journal = {Documenta mathematica},
     pages = {1863--1894},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/662},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/662/}
}
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Andreas Langer. $p$-Adic Deformation of Motivic Chow Groups. Documenta mathematica, Tome 23 (2018), pp. 1863-1894. doi: 10.4171/dm/662

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