On the Eisenstein symbol

Jörg Wildeshaus (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Domaines: K-théorie et homologie [math.KT]; Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Jörg Wildeshaus. On the Eisenstein symbol. Motives, polylogarithms and Hodge theory. Part I: Motives and polylogarithms., 1998, Irvine, CA, United States. ⟨hal-00012924⟩