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Number Theory and Discrete Mathematics pp 269–291Cite as

Birkhäuser

Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil

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Part of the book series: Trends in Mathematics ((TM))

Abstract

A brief survey of the conjectures of Weil and some classical estimates for the number of points of varieties over finite fields is given. The case of partial flag manifolds is discussed in some details by way of an example. This is followed by a motivated account of some recent results on counting the number of points of varieties over finite fields, and a related conjecture of Lang and Weil. Explicit combinatorial formulae for the Betti numbers and the Euler characteristics of smooth complete intersections are also discussed.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai, 400076, India

    Sudhir R. Ghorpade

  2. Équipe “Arithmétique et Théorie de l’Information”, Institut de Mathématiques de Luminy, Luminy Case 907, Marseille Cedex 9, 13288, France

    Gilles Lachaud

Authors
  1. Sudhir R. Ghorpade
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  2. Gilles Lachaud
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Editors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, 160014, India

    A. K. Agarwal

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© 2002 Springer Basel AG

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Ghorpade, S.R., Lachaud, G. (2002). Number of Solutions of Equations over Finite Fields and a Conjecture of Lang and Weil. In: Agarwal, A.K., Berndt, B.C., Krattenthaler, C.F., Mullen, G.L., Ramachandra, K., Waldschmidt, M. (eds) Number Theory and Discrete Mathematics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8223-1_27

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  • DOI: https://doi.org/10.1007/978-3-0348-8223-1_27

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9481-4

  • Online ISBN: 978-3-0348-8223-1

  • eBook Packages: Springer Book Archive

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