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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Alexander Beilinson

  2. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Guido Kings

  3. National Research University HSE, 7 Vavilova Str., Moscow, Russia

    Andrey Levin

Authors
  1. Alexander Beilinson
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  2. Guido Kings
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  3. Andrey Levin
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Corresponding author

Correspondence to Guido Kings.

Additional information

Communicated by Vasudevan Srinivas.

The authors research was partially supported by the following grants: NSF Grant DMS-1406734 (A.B.), DFG Grant SFB 1085 Higher invariants (G.K.), Simons-IUM Fellowship, Laboratory of Mirror Symmetry NRUHSE, RF Government grant, Ag. No. 14.641.31.0001 (A.L.).

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Beilinson, A., Kings, G. & Levin, A. Topological polylogarithms and p-adic interpolation of L-values of totally real fields. Math. Ann. 371, 1449–1495 (2018). https://doi.org/10.1007/s00208-018-1645-4

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  • DOI: https://doi.org/10.1007/s00208-018-1645-4

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