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:CHi(X/V,2iβn)βHsynnβ(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.Comment: 23 pages, improved expositio