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Geometric and topological aspects of the representation theory of finite groups : PIMS Summer School and Workshop, July 27-August 5, 2016

Author: J F Carlson; Srikanth Iyengar; Julia Pevtsova
Publisher: Cham : Springer, 2018.
Series: Springer proceedings in mathematics & statistics, v. 242.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at  Read more...
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Genre/Form: Conference papers and proceedings
Electronic books
Congresses
Additional Physical Format: Print version:
Carlson, Jon F.
Geometric and Topological Aspects of the Representation Theory of Finite Groups : PIMS Summer School and Workshop, July 27-August 5 2016.
Cham : Springer, ©2018
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J F Carlson; Srikanth Iyengar; Julia Pevtsova
ISBN: 9783319940335 3319940333 9783319940342 3319940341
OCLC Number: 1056895538
Description: 1 online resource (493 pages).
Contents: Intro; Preface; Contents; Restricting Homology to Hypersurfaces; 1 Differential Graded Algebra; 1.1 Tensor Products; 1.2 Divided Powers; 1.3 The Koszul Complex; 1.4 The Tate Construction; 1.5 Acyclic Closures; 2 Hypersurfaces; 2.1 Degree One Cycles; 2.2 Hypersurfaces; 3 Support Sets; 3.1 Support Sets; 3.2 Projective Dimension; 3.3 Alternative Description of Support; 3.4 Complexes over Regular Rings; 3.5 On Being Closed; 4 Defining Equations; 4.1 Complete Intersections; 5 Group Algebras of Elementary Abelian Groups; 5.1 Flat Dimension; 5.2 Rank Varieties; 5.3 Polynomial Extensions. 5.4 Nilpotent OperatorsReferences; Thick Subcategories of the Relative Stable Category; 1 Introduction; 2 Notation and Preliminaries; 3 Annihilators of Cohomology; 4 Additive Tensor Ideals; 5 Non-Noetherian Spectra; 6 Idempotent Modules; 7 Thick Subcategories by Inflation; 8 Empty Thick Tensor Ideals; 9 Examples; 10 One More Question; References; Nilpotent Elements in Hochschild Cohomology; 1 Introduction; 2 Preliminaries; 2.1 The Algebras; 2.2 Hochschild Cohomology; 2.3 Nilpotent Elements; 2.4 Independence of q; 3 A Minimal Bimodule Resolution; 3.1 The problem. 3.2 Relating to the one-sided resolution3.3 Minimal generators; 4 Homomorphisms and HHn(A); 4.1 Identities for homomorphisms; 4.2 The Proof of Proposition 4.3 for n+14; 4.3 Small Cases; References; Rational Cohomology and Supports for Linear Algebraic Groups; 1 Introduction; 2 Lecture I: Affine Group Schemes Over k; 2.1 Affine Group Schemes Over k; 2.2 Affine Group Schemes; 2.3 Characteristic p> 0; 2.4 Restricted Lie Algebras; 3 Lecture II: Algebraic Representations; 3.1 Algebraic Actions; 3.2 Examples; 3.3 Weights for G-Modules; 3.4 Representations of Frobenius Kernels. 4 Lecture III: Cohomological Support Varieties4.1 Indecomposable Versus Irreducible; 4.2 Derived Functors; 4.3 The Quillen Variety G and the Cohomological Support Variety GM; 5 Lecture IV: Support Varieties for Linear Algebraic Groups; 5.1 1-Parameter Subgroups; 5.2 p-Nilpotent Operators; 5.3 The Support Variety V(G)M; 5.4 Classes of Rational G-Modules; 5.5 Some Questions of Possible Interest; References; Anderson and Gorenstein Duality; 1 Introduction; 1.1 Motivation; 1.2 Description of Contents; 1.3 Conventions; 2 Anderson Duals; 2.1 Construction of Brown-Comenetz Duals. 2.2 Properties of Brown-Comenetz Duals2.3 Construction of Anderson Duals; 2.4 Properties of Anderson Duals; 3 The Gorenstein Condition; 3.1 Cellularization; 3.2 Morita Theory; 3.3 The Gorenstein Condition; 3.4 Gorenstein Duality; 3.5 Gorenstein Duality Relative to mathbbFp; 3.6 Mahowald-Rezk Duality; 4 Gorenstein Duality and Anderson Self-duality; 4.1 Nullifying HK; 4.2 Anderson Self-duality from Gorenstein Duality; 4.3 Gorenstein Duality from Anderson Self-duality; 5 Examples with Polynomial or Hypersurface Coefficient Rings; 5.1 The Čech Complex; 5.2 The Algebraic Context.
Series Title: Springer proceedings in mathematics & statistics, v. 242.
Responsibility: Jon F. Carlson, Srikanth B. Iyengar, Julia Pevtsova, editors.

Abstract:

The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the  Read more...

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