Nombre de points des surfaces de Deligne et Lusztig

Resume On etudie dans ce travail des exemples de surfaces algebriques sur un corps fini qui ont beaucoup de points relativement a leurs nombres de Betti et qui ont un groupe d'automorphismes important. Ces exemples sont construits a partir des varietes de Deligne et Lusztig. We present examples of algebraic surfaces on a finite field with many points with respect to their Betti numbers and with a large automorphism group. These examples are constructed from Deligne–Lusztig varieties.

[1]  J. Humphreys,et al.  Linear Algebraic Groups , 1975 .

[2]  Michael Rosen,et al.  A classical introduction to modern number theory , 1982, Graduate texts in mathematics.

[3]  B. Srinivasan Representations of Finite Chevalley Groups , 1979 .

[4]  I. Shafarevich Basic algebraic geometry , 1974 .

[5]  D. Mumford,et al.  Complex Analysis and Algebraic Geometry: Enriques' Classification of Surfaces in Char. p , II , 1977 .

[6]  G. Lusztig,et al.  Representations of reductive groups over finite fields , 1976 .

[7]  Johan P. Hansen,et al.  Deligne-Lusztig varieties and group codes , 1992 .

[8]  Meinolf Geck,et al.  Finite groups of Lie type , 1985 .

[9]  P. Deligne La conjecture de Weil. I , 1974 .

[10]  Michael A. Tsfasman Nombre de points des surfaces sur un corps fini , 1996 .

[11]  D. Mumford,et al.  Enriques' classification of surfaces in char.p, III , 1976 .

[12]  G. Lusztig On the Green Polynomials of Classical Groups , 1976 .

[13]  Phillip A. Griffiths,et al.  Complex analysis and algebraic geometry , 1979 .

[14]  Michael A. Tsfasman,et al.  Formules explicites pour le nombre de points des varits sur un corps fini. , 1997 .

[15]  Henning Stichtenoth,et al.  Algebraic function fields and codes , 1993, Universitext.

[16]  A. Weil Numbers of solutions of equations in finite fields , 1949 .

[17]  I. G. MacDonald,et al.  Lectures on Lie Groups and Lie Algebras: Simple groups of Lie type , 1995 .

[18]  G. Lusztig Coxeter orbits and eigenspaces of Frobenius , 1976 .

[19]  R. C. Bose,et al.  Hermitian Varieties in a Finite Projective Space PG(N, q 2) , 1966, Canadian Journal of Mathematics.