Equivariant Poincaré polynomials and counting points over finite fields

DOI10.1006/jabr.2001.9029zbMath1039.14005OpenAlexW1974160549MaRDI QIDQ1348675

Gustav Isaac Lehrer, Mark Kisin

Publication date: 2002

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.9029

zbMATH Keywords

Poincaré polynomials\(\ell\)-adic cohomologysmooth schemeaction of groupaction on cohomologyequivariant comparisonnumbers of rational points

Mathematics Subject Classification ID

Group actions on varieties or schemes (quotients) (14L30) Rational points (14G05) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Classical real and complex (co)homology in algebraic geometry (14F25) Finite ground fields in algebraic geometry (14G15) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) (p)-adic cohomology, crystalline cohomology (14F30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Imbedding of an abstract variety in a complete variety
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant
• The cohomology of the regular semisimple variety
• Regular elements of finite reflection groups
• Poincaré polynomials for unitary reflection groups
• The tree representation of \(\Sigma_{n+1}\)
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Cohomology Actions and Centralisers in Unitary Reflection Groups
• On the Poincaré Series Associated with Coxeter Group Actions on Complements of Hyperplanes
• The l Adic Cohomology of Hyperplane Complements
• Operads and moduli spaces of genus $0$ Riemann surfaces
• Generating Functions in Algebraic Geometry and Sums over Trees
• Homology stability for classical regular semisimple varieties.