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Israel Journal of Mathematics

, Volume 190, Issue 1, pp 29–66 | Cite as

On the syntomic regulator for K 1 of a surface

  • Amnon Besser
Article

Abstract

We consider elements of K 1(S), where S is a proper surface over a p-adic field with good reduction, which are given by a formal sum Σ(Z i , f i ) with Z i curves in S and f i rational functions on the Z i in such a way that the sum of the divisors of the f i is 0 on S. Assuming compatibility of pushforwards in syntomic and motivic cohomologies, our result computes the syntomic regulator of such an element, interpreted as a functional on H dR 2 (S), when evaluated on the cup product ω∪[η] of a holomorphic form ω by the first cohomology class of a form of the second kind η. The result is Σ i F η , log(f i ); F ω gl,Z i , where F ω and F η are Coleman integrals of ω and η, respectively, and the symbol in brackets is the global triple index, as defined in our previous work.

Keywords

Cohomology Class Short Exact Sequence Cohomology Theory Chern Character Projection Formula 
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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBe’er-ShevaIsrael

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