Skip to main content
SpringerLink
Log in

Zeta-Functions of Varieties Over Finite Fields at s=1

  • Chapter
Arithmetic and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 35))

Abstract

Let κ be a finite field of cardinality q = p ’. Let \(\overline \kappa \) be a fixed algebraic closure of κ. Let X be a smooth projective algebraic variety of dimension d over κ such that \(\overline X = X \times \overline \kappa \) is connected.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Deligne, P. La conjecture de Weil, I. Publ. Math. I.H.B.S. 43 (1974), 273–307.

    MathSciNet  Google Scholar 

  2. Gabber, O. Sur la torsion dans la cohomologie l-adique d’une variété (to appear).

    Google Scholar 

  3. Kaplansky, I. Infinite Abelian Groups, University of Michigan Press, Ann Arbor (1954).

    Google Scholar 

  4. Milne, J.S. On a conjecture of Artin and Tate, Ann of Math. 102 (1975), 517–533.

    Article  MathSciNet  MATH  Google Scholar 

  5. Milne, J.S. Etale Cohomology, Princeton University Press, Princeton, (1980).

    Google Scholar 

  6. Mumford, D. Abelian Varieties, Oxford University Press, London (1970).

    MATH  Google Scholar 

  7. Tate, J. On a conjecture of Birch and Swinnerton-Dyer and a geometric analogue. Seminaire Bourbaki no. 306, 1965–66, W.A. Benjamin Inc. (1966).

    Google Scholar 

  8. Tate, J. Algebraic cycles and poles of zeta-functions. Arithmetic Algebraic Geometry, Harper and Row, New York, (1965).

    Google Scholar 

  9. Zarchin, Yu. G. The Brauer group of abelian varieties over finite fields, (in Russian) Izv. Akad. Nauk. USSR 46 (1980), 211–243. Received June 30, 1982 Partially supported by N.S.F. grants

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, New York, 14853, USA

    Professor Stephen Lichtenbaum

Authors
  1. Professor Stephen Lichtenbaum
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematics Department, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Michael Artin

  2. Mathematics Department, Harvard University, 02138, Cambridge, MA, USA

    John Tate

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lichtenbaum, S. (1983). Zeta-Functions of Varieties Over Finite Fields at s=1. In: Artin, M., Tate, J. (eds) Arithmetic and Geometry. Progress in Mathematics, vol 35. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-9284-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9284-3_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3132-1

  • Online ISBN: 978-1-4757-9284-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation