2001/10/31 by Amnon Besser, Besser, Amnon, Rob de Jeu +1
Mathematics · #11G55 #11S70 #14F30 (Secondary) #19F27 (Primary) 11S80 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.AG #math.KT #math.NT #msc:11G55 #msc:11S70 #msc:11S80 #msc:14F30 #msc:19F27
paper · pdf · doi:10.48550/arxiv.math/0110334
53 pages, latex2e with amsart class, xypic, minor changes
arxiv created 2001/12/15 · arxiv updated 2009/11/30
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.