Topological polylogarithms and $p$-adic interpolation of $L$-values of totally real fields

Abstract

We develop the topological polylogarithm which provides an integral version of Nori's Eisenstein cohomology classes for $G{L}_n(\mathbf{Z})$ and yields classes with values in an Iwasawa algebra. This implies directly the integrality properties of special values of $L$-functions of totally real fields and a construction of the associated $p$-adic $L$-function. Using a result of Graf, we also apply this to prove some integrality and $p$-adic interpolation results for the Eisenstein cohomology of Hilbert modular varieties.

32 pages

References in corpus (1)

• Rankin--Eisenstein classes and explicit reciprocity laws

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