On the Eisenstein symbol

Details On the Eisenstein symbol On the Eisenstein symbol

2000-06-22

arxiv.org/abs/math/0006170v1

Mathematics

K-Theory and Homology

119 pages

Scientific paper

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.

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