On the Eisenstein symbol, by Joerg Wildeshaus

The main purpose of this paper is the geometric construction, and the analysis of the formalism of elliptic Bloch groups. In the setting of absolute cohomology, we obtain a generalization of Beilinson's Eisenstein symbol to divisors of an elliptic curve, whose support is not necessarily torsion. For motivic cohomology, such a generalization is obtained in low degrees. Our main result shows that the Eisenstein symbol can be defined in all degrees if the elliptic analogue of the Beilinson-Soule vanishing conjecture holds.

This paper is the final version of #213. The main improvement is that the main results no longer require an injectivity statement on the (product of the) regulators.


Joerg Wildeshaus <wildesh@zeus.math.univ-paris13.fr>