The syntomic regulator for K-theory of fields

Details The syntomic regulator for K-theory of fields The syntomic regulator for K-theory of fields

2001-10-31

arxiv.org/abs/math/0110334v2

Mathematics

Algebraic Geometry

53 pages, latex2e with amsart class, xypic, minor changes

Scientific paper

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the ring. In case the ring is the localization of the ring of integers in a number field, there are no assumptions necessary. We compute the composition of our map to the K-theory with the syntomic regulator. The result can be described in terms of a p-adic polylogarithm. Finally, we apply our theory in order to compute the regulator to syntomic cohomology on Beilinson's cyclotomic elements. The result is again given by the p-adic polylogarithm. This last result is related to one by Somekawa and generalizes work by Gros.

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