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Cycle classes and the
syntomic regulator
Bruno Chiarellotto, Alice Ciccioni and Nicola Mazzari |
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Vol. 7 (2013), No. 3, 533–566
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Abstract |
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Let and be a complete discrete valuation ring of mixed characteristic . For any flat -scheme , 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 when is smooth over 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
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Mathematical Subject Classification 2010
Primary: 14F43
Secondary: 14F30, 19F27
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Milestones
Received: 12 October 2010
Revised: 22 December 2011
Accepted: 3 May 2012
Published: 23 August 2013
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Authors |
| Bruno Chiarellotto | |
| Università degli Studi di
Padova Via Trieste 63 35100 Padova Italy |
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| Alice Ciccioni | |
| Università degli Studi di
Padova Via Trieste 63 35100 Padova Italy |
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| Nicola Mazzari | |
| IMB Université Bordeaux 1 351, cours de la Libération 33405 Talence cedex France |
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