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General Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 900)

Abstract

Let X be a smooth projective variety over ℂ. Hodge conjectured that certain cohomology classes on X are algebraic. The work of Deligne that is described in the first article of this volume shows that, when X is an abelian variety, the classes considered by Hodge have many of the properties of algebraic classes.

Keywords

  • Cohomology Class
  • Abelian Variety
  • Hodge Structure
  • Serre Group
  • Algebraic Cycle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-540-38955-2_10

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References

  1. Langlands, R., Some contemporary problems with origins in the Jugendtraum. Proc. Symp. Pure Math., A.M.S. 28 (1976) 401–418.

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  2. Langlands, R., Automorphic representations, Shimura varieties, and motives. Ein Märchen. Proc. Symp. Pure Math., A.M.S., 33 (1979) part 2 205–246.

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  3. Saavedra Rivano, N., Catégories Tannakiennes, Lecture Notés in Math 265 Springer, Heidelberg 1972.

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© 1982 Springer-Verlag Berlin Heidelberg

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Deligne, P., Milne, J.S., Ogus, A., Shih, Ky. (1982). General Introduction. In: Hodge Cycles, Motives, and Shimura Varieties. Lecture Notes in Mathematics, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38955-2_1

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  • DOI: https://doi.org/10.1007/978-3-540-38955-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11174-0

  • Online ISBN: 978-3-540-38955-2

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