### 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 language | English |
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Title of host publication | Commutative Algebra and Noncommutative Algebraic Geometry |

Subtitle of host publication | Volume II: Research Articles |

Editors | David Eisenbud, Srikanth Iyengar, Anurag Singh, Toby Stafford, Michel Van den Bergh |

Place of Publication | New York |

Publisher | Cambridge University Press |

Pages | 19-42 |

Number of pages | 24 |

Volume | 68 |

ISBN (Print) | 978-1-107-14972-4 |

Publication status | Published - 2015 |

### Publication series

Name | Mathematical Sciences Research Institute Publications |
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Publisher | Cambridge University Press |

Volume | 68 |

## Fingerprint Dive into the research topics of 'Modules for elementary abelian groups and hypersurface singularities'. Together they form a unique fingerprint.

## 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). Cambridge University Press.