Abstract Johannes Sprang

Johannes Sprang will speak on

A geometric construction of the de Rham realization of the elliptic polylogarithm

Abstract: In order to prove particular cases of conjectures like the Tamagawa number conjecture of Bloch and Kato on special values of L-functions one needs a good understanding of K-theory classes and their realizations. One tool to construct such classes is the elliptic polylogarithm. In this talk we will focus on its de Rham realization.

We start with recalling the universal property of the logarithm sheaves and the definition of the elliptic polylogarithm. Then we recall a geometric construction of the logarithm sheaves via Fourier-Mukai transforms due to R. Scheider. This anables us to give a geometric construction of the elliptic polylogarithm in the de Rham setting. Its specialization along torsion sections is related to Eisenstein series.

In ongoing work we want to exploit the above geometric situation to prove an explicit reciprocity law for CM elliptic curves.