CHIARELLOTTO, Bruno; CICCIONI, Alice; MAZZARI, Nicola

doi:10.2140/ant.2013.7.533

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CHIARELLOTTO, Bruno
Dipartimento di Matematica Pura e Applicata [Padova]

CICCIONI, Alice
Dipartimento di Matematica Pura e Applicata [Padova]

MAZZARI, Nicola
Institut de Mathématiques de Bordeaux [IMB]

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Algebra & Number Theory. 2013, vol. 7, n° 3, p. 533-566

Mathematical Sciences Publishers

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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 $r:CH^i(X/V,2i-n)\to H^n_{syn}(X,i)$, when $X$ is smooth over $V$, with values on 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.< Leer menos

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Cycle classes and the syntomic regulator

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