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On Poly(ana)logs I

Published online by Cambridge University Press:  04 December 2007

Philippe Elbaz-Vincent  and
Herbert Gangl
Philippe Elbaz-Vincent
Affiliation:
Laboratoire GTA, UMR CNRS 5030, CC 051, Université Montpellier II, 34095 Montpellier Cedex 5, France. E-mail: pev@math.univ-montp2.fr
Herbert Gangl
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany. E-mail: herbert@mpim-bonn.mpg.de
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Abstract

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We investigate a connection between the differential of polylogarithms (as considered by Cathelineau) and a finite variant of them. This allows to answer a question raised by Kontsevich concerning the construction of functional equations for the finite analogs, using in part the p-adic version of polylogarithms and recent work of Besser. Kontsevich's original unpublished note is supplied (with his kind permission) in an ‘Appendix’ at the end of the paper.

Keywords

polylogarithmsinfinitesimal polylogarithmspolylogarithms over finite fieldsp-adic polylogarithmsfunctional equationsderivationsdifferentialBloch groupGoncharov complexes
Type
Research Article
Information
Compositio Mathematica , Volume 130 , Issue 2 , January 2002 , pp. 161 - 214
Copyright
© 2002 Kluwer Academic Publishers