Degeneration of the l-adic Eisenstein symbol and of the elliptic polylog, by Annette Huber and Guido Kings

We construct elements in K-theory of cyclotomic fields using the Eisenstein symbol on modular curves. The image under the l-adic regulator is given by the degeneration of l-adic Eisenstein classes. They can be computed explicitly by studying the degeneration of the elliptic polylog.

Together with the Hodge theoretic computation in a previous paper (Dirichlet motives via modular curves, on this server), we get a new proof of a comparison conjecture of Bloch and Kato which was used in the proof of their Tamagawa number conjecture for the Riemann zeta-function.

This article has appeared in Inventiones Mathematicae, Volume 135 Issue 3 (1999) pp 545-594.

Annette Huber <>
Guido Kings <>