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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.
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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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