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Counting points of homogeneous varieties over finite fields
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Michel Brion
Published/Copyright:
August 11, 2010
Abstract
Let X be an algebraic variety over a finite field 𝔽q, homogeneous under a linear algebraic group. We show that there exists an integer N such that for any positive integer n in a fixed residue class mod N, the number of rational points of X over 𝔽qn is a polynomial function of qn with integer coefficients. Moreover, the shifted polynomials, where qn is formally replaced with qn + 1, have non-negative coefficients.
Received: 2008-09-17
Revised: 2009-04-11
Published Online: 2010-08-11
Published in Print: 2010-August
© Walter de Gruyter Berlin · New York 2010
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- La filtration de Harder-Narasimhan des schémas en groupes finis et plats
- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
- Counting points of homogeneous varieties over finite fields
- Noncompact shrinking four solitons with nonnegative curvature
- Free analysis questions II: The Grassmannian completion and the series expansions at the origin
Articles in the same Issue
- La filtration de Harder-Narasimhan des schémas en groupes finis et plats
- Formules de caractères pour l'induction automorphe
- Duality theorems for slice hyperholomorphic functions
- Counting points of homogeneous varieties over finite fields
- Noncompact shrinking four solitons with nonnegative curvature
- Free analysis questions II: The Grassmannian completion and the series expansions at the origin
