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- Title
Counting points of homogeneous varieties over finite fields.
- Authors
Brion, Michel; Peyre, Emmanuel
- Abstract
Let X be an algebraic variety over a finite field q, 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 qn 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.
- Subjects
ALGEBRAIC fields; GROUP theory; ALGEBRAIC varieties; RATIONAL points (Geometry); ARITHMETICAL algebraic geometry; LINEAR algebraic groups
- Publication
Journal für die Reine und Angewandte Mathematik, 2010, Vol 2010, Issue 645, p105
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/CRELLE.2010.061