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Mathematische Annalen

, Volume 371, Issue 3–4, pp 1449–1495 | Cite as

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

  • Alexander Beilinson
  • Guido KingsEmail author
  • Andrey Levin
Article
  • 197 Downloads

Abstract

We develop the topological polylogarithm which provides an integral version of Nori’s Eisenstein cohomology classes for \({{\mathrm{GL}}}_n(\mathbb {Z})\) 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.

Notes

Acknowledgements

A. Beilinson would like to thank M. Nori for the introduction to his Eisenstein cohomology classes back in 1992. G. Kings would like to thank the University of Chicago for a very profitable stay in 2002. He also would like to thank M. Nori for discussions at that time about the possibility to construct Harder’s Eisenstein classes for Hilbert modular varieties with Nori’s \({{\mathrm{GL}}}_n(\mathbb {Z})\) cohomology classes. The authors would also like to thank the referee for very useful suggestions.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Beilinson
    • 1
  • Guido Kings
    • 2
    Email author
  • Andrey Levin
    • 3
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  3. 3.National Research University HSEMoscowRussia

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