With cedram.org
Confluentes Mathematici
Search for an article
Search within the site
Table of contents for this issue | Next article
Philippe Caldero
Cône nilpotent sur un corps fini et $q$-séries hypergéométriques
(Nilpotent cone over a finite field and hypergeometric $q$-series)
Confluentes Mathematici, 8 no. 2 (2016), p. 3-22, doi: 10.5802/cml.30
Article PDF
Class. Math.: 05A30, 05A19, 05B25, 05E15, 19F27
Keywords: Corps finis, cône nilpotent, fonctions hypergéométriques, conjectures de Weil

Résumé - Abstract

We present different methods to compute the size of various nilpotent cones over a finite field. We insist in particular on the role hypergeometric functions play in these computations. To finish, we give a cohomological interpretation of our results.


[1] Walter Borho & Robert MacPherson, “Partial resolutions of nilpotent varieties”, Astérisque 101 (1983) no. 102, p. 23-74
[2] Michel Brion, Equivariant cohomology and equivariant intersection theory, Representation theories and algebraic geometry, Springer, 1998, p. 1–37
[3] Andries E Brouwer, Rod Gow & John Sheekey, “Counting symmetric nilpotent matrices”, The Electronic Journal of Combinatorics 21 (2014) no. 2, p. P2-4
[4] Philippe Caldero & Frédéric Chapoton, “Cluster algebras as Hall algebras of quiver representations”, arXiv preprint math/0410187 (2004)
[5] Philippe Caldero & Jérôme Germoni, “Histoires hédonistes de groupes et de géométries, Tome premier” 2012
[6] Philippe Caldero & Jérôme Germoni, “Histoires hédonistes de groupes et de géométries, Tome second” 2014
[7] NJ Fine, IN Herstein & , “The probability that a matrix be nilpotent”, Illinois Journal of Mathematics 2 (1958) no. 4A, p. 499-504
[8] Karl Friedrich Gauß, Disquisitiones generales circa seriem infinitam, Dieterich, 1813
[9] Frances Kirwan & Jonathan Woolf, An introduction to intersection homology theory, CRC Press, 2006
[10] James S Milne, Etale Cohomology (PMS-33), Princeton University Press, 1980
eISSN : 1793-7434