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ON THE RESIDUE OF EISENSTEIN CLASSES OF SIEGEL VARIETIES

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  30 October 2017

FRANCESCO LEMMA Open the ORCID record for FRANCESCO LEMMA [Opens in a new window]
FRANCESCO LEMMA*
Affiliation:
Institut mathématique de Jussieu-Paris Rive Gauche, UMR 7586, Bâtiment Sophie Germain, Case 7012, 75205 Paris Cedex 13, France e-mail: francesco.lemma@imj-prg.fr
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Abstract

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Eisenstein classes of Siegel varieties are motivic cohomology classes defined as pull-backs by torsion sections of the polylogarithm prosheaf on the universal abelian scheme. By reduction to the Hilbert–Blumenthal case, we prove that the Betti realization of these classes on Siegel varieties of arbitrary genus have non-trivial residue on zero-dimensional strata of the Baily–Borel–Satake compactification. A direct corollary is the non-vanishing of a higher regulator map.

MSC classification

Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 14G35: Modular and Shimura varieties
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 3 , September 2018 , pp. 539 - 553
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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