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Suslin Homology and Deligne 1-Motives

Chapter
Part of the NATO ASI Series book series (ASIC, volume 407)

Abstract

Suslin has defined a complex for any algebraic variety X over an algebraically closed field k which computes what he calls the “algebraic homology” of X. If X is an arbitrary curve C, we show that this complex may be viewed as the points of a “homology motive” of C with values in k.

Keywords

Abelian Group Exact Sequence Abelian Variety Algebraic Topology Free Abelian Group 
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References

  1. [D]
    Deligne, P., Theorie de Hodge, III, Publ. Math. IRES 44 (1974), 5 - 77.zbMATHGoogle Scholar
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    Lichtenbaum, S., Motivic Complexes, Proceedings of the American Mathematical Society Conference on Motives, Seattle 1991.Google Scholar
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    May, J. Peter, Simplicial Objects in Algebraic Topology. D. Van Nostrand Company, Inc., Princeton, 1967.Google Scholar
  4. [N]
    Nart, E., The Bloch Complex in Codimension One and Arithmetic Duality, Journal of Number Theory 32 (1989), 321 - 331.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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