Geodesic
A $p$-adic regulator map and finiteness results for arithmetic schemes
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 525-594.

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

A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is related to finiteness of two arithmetic objects: One is the $p$-primary torsion part of the Chow group in codimension 2 of $X$. Another is an unramified cohomology group of $X$. As an application, for a regular model ${\cal X}$ of $X$ over the integer ring of $k$, we prove an injectivity result on the torsion cycle class map of codimension 2 with values in a new $p$-adic cohomology of ${\cal X}$ introduced by the second author, which is a candidate of the conjectural étale motivic cohomology with finite coefficients of Beilinson-Lichtenbaum.
Classification : 14C25, 14G40, 14F30, 19F27, 11G25
Keywords: $p$-adic regulator, unramified cohomology, Chow groups, $p$-adic étale Tate twists 
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     title = {A $p$-adic regulator map and finiteness results for arithmetic schemes},
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Saito, S.; Sato, K. A $p$-adic regulator map and finiteness results for arithmetic schemes. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 525-594. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a5/