The elliptic polylogarithm. (English) Zbl 0817.14014

Beilinson, A.; Levin, A.

Jannsen, Uwe (ed.) et al., Motives. Proceedings of the summer research conference on motives, held at the University of Washington, Seattle, WA, USA, July 20-August 2, 1991. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 55, Pt. 2, 123-190 (1994).

The paper constructs an elliptic analogue of the polylogarithm. These occur as analytic trivialisations of certain sheaves, which are universal objects in the category of “unipotent sheaves”. In arithmetic these define motivic cohomology-classes. The construction has some similarity with a previous one of the first author [in: Applications of algebraic \(K\)-theory to algebraic geometry and number theory, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Boulder/Colo. 1983, Part I, Contemp. Math. 55, 1-34 (1986; Zbl 0609.14006)], and at least the regulators coincide.
For the entire collection see [Zbl 0788.00054].

Reviewer: G.Faltings (Bonn)

MSC:

14H52	Elliptic curves
11G05	Elliptic curves over global fields
14A20	Generalizations (algebraic spaces, stacks)
19F27	Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)
14C35	Applications of methods of algebraic \(K\)-theory in algebraic geometry

Keywords:

unipotent sheaves; an elliptic analogue of the polylogarithm; motivic cohomology classes; regulator