Presentations

The Beilinson conjecture for algebraic varieties and more general motives defined over algebraic number fields is a conjecture relating the non-critical values of Hasse-Weil L-functions to regulator of certain elements in motivic cohomology. For the case of the Dirichlet L-function for the rational number field Q, the special value is related to the regulator of the cyclotomic element -- which may be constructed as the specialization to torsion points of the motivic polylogarithm in this case. In order to prospect p-adic analogues of such results in the case of totally real fields, we consider the syntomic realization of the polylogarithm for the algebraic torus associated to a totally real field, and its relation to special values of p-adic L-functions associated to Hecke characters of the totally real field. This is a work in process, and includes results of work with H. Bekki, K. Hagihara, T. Oshita, K. Yamada, and S. Yamamoto.