Modules for elementary abelian groups and hypersurface singularities

David John Benson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

ThispaperisaversionofthelectureIgaveattheconferenceon“Representation Theory, Homological Algebra and Free Resolutions” at MSRI in February 2013, expanded to include proofs. My goals in this lecture were to explain to an audience of commutative algebraists why a finite group representation theorist might be interested in zero dimensional complete intersections, and to give a version of the Orlov correspondence in this context that is well suited to computation. In the context of modular representation theory, this gives an equivalence between the derived category of an elementary abelian p-group of rank r, and the category of (graded) reduced matrix factorisations of the polynomial y1X1p +···+yrXrp. Finally, I explain the relevance to some recent joint work with Julia Pevtsova on realisation of vector bundles on projective space from modular representations of constant Jordan type.
Original languageEnglish
Title of host publicationCommutative Algebra and Noncommutative Algebraic Geometry
Subtitle of host publicationVolume II: Research Articles
EditorsDavid Eisenbud, Srikanth Iyengar, Anurag Singh, Toby Stafford, Michel Van den Bergh
Place of PublicationNew York
PublisherCambridge University Press
Pages19-42
Number of pages24
Volume68
ISBN (Print)978-1-107-14972-4
Publication statusPublished - 2015

Publication series

NameMathematical Sciences Research Institute Publications
PublisherCambridge University Press
Volume68

Fingerprint

Modular Representations
Abelian group
Hypersurface
Algebraist
Singularity
Factorization of Matrices
Free Resolution
Module
Group Representation
Derived Category
Zero-dimensional
Complete Intersection
P-groups
Representation Theory
Projective Space
Vector Bundle
Finite Group
Correspondence
Equivalence
Algebra

Cite this

Benson, D. J. (2015). Modules for elementary abelian groups and hypersurface singularities. In D. Eisenbud, S. Iyengar, A. Singh, T. Stafford, & M. Van den Bergh (Eds.), Commutative Algebra and Noncommutative Algebraic Geometry: Volume II: Research Articles (Vol. 68, pp. 19-42). [2] (Mathematical Sciences Research Institute Publications; Vol. 68). New York: Cambridge University Press.

Modules for elementary abelian groups and hypersurface singularities. / Benson, David John.

Commutative Algebra and Noncommutative Algebraic Geometry: Volume II: Research Articles. ed. / David Eisenbud; Srikanth Iyengar; Anurag Singh; Toby Stafford; Michel Van den Bergh. Vol. 68 New York : Cambridge University Press, 2015. p. 19-42 2 (Mathematical Sciences Research Institute Publications; Vol. 68).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Benson, DJ 2015, Modules for elementary abelian groups and hypersurface singularities. in D Eisenbud, S Iyengar, A Singh, T Stafford & M Van den Bergh (eds), Commutative Algebra and Noncommutative Algebraic Geometry: Volume II: Research Articles. vol. 68, 2, Mathematical Sciences Research Institute Publications, vol. 68, Cambridge University Press, New York, pp. 19-42.
Benson DJ. Modules for elementary abelian groups and hypersurface singularities. In Eisenbud D, Iyengar S, Singh A, Stafford T, Van den Bergh M, editors, Commutative Algebra and Noncommutative Algebraic Geometry: Volume II: Research Articles. Vol. 68. New York: Cambridge University Press. 2015. p. 19-42. 2. (Mathematical Sciences Research Institute Publications).
Benson, David John. / Modules for elementary abelian groups and hypersurface singularities. Commutative Algebra and Noncommutative Algebraic Geometry: Volume II: Research Articles. editor / David Eisenbud ; Srikanth Iyengar ; Anurag Singh ; Toby Stafford ; Michel Van den Bergh. Vol. 68 New York : Cambridge University Press, 2015. pp. 19-42 (Mathematical Sciences Research Institute Publications).
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