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2013 Cycle classes and the syntomic regulator
Bruno Chiarellotto, Alice Ciccioni, Nicola Mazzari
Algebra Number Theory 7(3): 533-566 (2013). DOI: 10.2140/ant.2013.7.533


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,2in)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.


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Bruno Chiarellotto. Alice Ciccioni. Nicola Mazzari. "Cycle classes and the syntomic regulator." Algebra Number Theory 7 (3) 533 - 566, 2013.


Received: 12 October 2010; Revised: 22 December 2011; Accepted: 3 May 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1330.14030
MathSciNet: MR3095220
Digital Object Identifier: 10.2140/ant.2013.7.533

Primary: 14F43
Secondary: 14F30 , 19F27

Keywords: cycles , de Rham cohomology , regulator map , rigid cohomology , syntomic cohomology

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.7 • No. 3 • 2013
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