Monatshefte für Mathematik

, Volume 135, Issue 3, pp 221–244

On Cycles on Compact Locally Symmetric Varieties

  • T. N. Venkataramana

DOI: 10.1007/s006050200018

Cite this article as:
Venkataramana, T. Mh Math (2002) 135: 221. doi:10.1007/s006050200018


 We give a criterion to determine when the cycle class of a locally symmetric subvariety \(\) of a compact locally symmetric variety \(\) generates a non-trivial module under the action of Hecke operators, and give several examples where this criterion is satisfied. We also exhibit examples of subvarieties \(\) which do generate the trivial module under the action of Hecke operators. We show that all Hodge classes (in degree \(\)) on the locally symmetric variety \(\) associated to certain arithmetric subgroups Γ of \(\) are algebraic (provided that \(\)).

2000 Mathematics Subject Classification: 11G18; 11F16 11F55 14G35 22E55 
Key words: Locally symmetric varieties Hodge classes 

Copyright information

© Springer-Verlag Wien 2002

Authors and Affiliations

  • T. N. Venkataramana
    • 1
  1. 1.Tata Institute of Fundamental Research, Colaba, Mumbai, IndiaIN

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