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The syntomic regulator for the K-theory of fields.

Besser, A. and de Jeu, R. (2003) 'The syntomic regulator for the K-theory of fields.', Annales scientifiques de l'ecole normale superieure., 36 (6). pp. 867-924.


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 under consideration. In case the ring is a 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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Record Created:01 May 2007
Last Modified:02 Aug 2017 16:30

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