Vol. 260, No. 2, 2012

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The syntomic regulator for K4 of curves

Amnon Besser and Rob de Jeu

Vol. 260 (2012), No. 2, 305–380
Abstract

Let C be a curve defined over a complete discrete valuation subfield of p. Assuming that C has good reduction over the residue field, we compute the syntomic regulator on a certain part of K4(3)(C). The result can be expressed in terms of p-adic polylogarithms and Coleman integration. We also compute the syntomic regulator on a certain part of K4(3)(F) for the function field F of C. The result can be expressed in terms of p-adic polylogarithms and Coleman integration, or by using a trilinear map (“triple index”) on certain functions.

Keywords
algebraic K-theory, syntomic regulator, p-adic polylogarithm
Mathematical Subject Classification 2010
Primary: 11G55, 14F42, 19E08, 19F27
Secondary: 11G20, 14F30, 19E20
Milestones
Received: 21 July 2012
Accepted: 4 October 2012
Published: 30 November 2012
Authors
Amnon Besser
Department of Mathematics
Ben-Gurion University of the Negev
P.O.B. 653
84105 Be’er-Sheva
Israel
http://www.math.bgu.ac.il/~bessera/
Rob de Jeu
Faculteit der Exacte Wetenschappen, Afdeling Wiskunde
VU University Amsterdam
De Boelelaan 1081a
1081 HV Amsterdam
Netherlands
http://www.few.vu.nl/~jeu/