Vol. 7, No. 3, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Cycle classes and the syntomic regulator

Bruno Chiarellotto, Alice Ciccioni and Nicola Mazzari

Vol. 7 (2013), No. 3, 533–566
Abstract

Let V = Spec(R) and R be a complete discrete valuation ring of mixed characteristic (0,p). For any flat R-scheme X, we prove the compatibility of the de Rham fundamental class of the generic fiber and the rigid fundamental class of the special fiber. We use this result to construct a syntomic regulator map regsyn : CHi(XV,2i n) Hsynn(X,i) when X is smooth over R with values in the syntomic cohomology defined by A. Besser. Motivated by the previous result, we also prove some of the Bloch–Ogus axioms for the syntomic cohomology theory but viewed as an absolute cohomology theory.

Keywords
syntomic cohomology, cycles, regulator map, rigid cohomology, de Rham cohomology
Mathematical Subject Classification 2010
Primary: 14F43
Secondary: 14F30, 19F27
Milestones
Received: 12 October 2010
Revised: 22 December 2011
Accepted: 3 May 2012
Published: 23 August 2013
Authors
Bruno Chiarellotto
Università degli Studi di Padova
Via Trieste 63
35100 Padova
Italy
Alice Ciccioni
Università degli Studi di Padova
Via Trieste 63
35100 Padova
Italy
Nicola Mazzari
IMB
Université Bordeaux 1 351, cours de la Libération
33405 Talence cedex
France