On poly(ana)logs I

Elbaz-Vincent, Ph; Gangl, H.

Abstract

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 Kontsevich's original unpublished note is supplied (with his kind permission) in an ``Appendix'' at the end of the paper.

Citation

Elbaz-Vincent, P., & Gangl, H. (2002). On poly(ana)logs I. Compositio Mathematica, 130(2), 161-214. https://doi.org/10.1023/a%3A1013757217319

• Journal Article Type: Article
• Publication Date: 2002-01
• Deposit Date: Mar 20, 2008
• Journal: Compositio Mathematica
• Print ISSN: 0010-437X
• Electronic ISSN: 1570-5846
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 130
• Issue: 2
• Pages: 161-214
• DOI: https://doi.org/10.1023/a%3A1013757217319
• Keywords: Polylogarithms, Finite fields, p-adic, Functional equations, Derivations, Bloch group, Goncharov complexes.