### Abstract

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 |
---|---|

Publisher | Cambridge University Press |

Volume | 68 |

### Fingerprint

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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.

}

TY - GEN

T1 - Modules for elementary abelian groups and hypersurface singularities

AU - Benson, David John

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

M3 - Conference contribution

SN - 978-1-107-14972-4

VL - 68

T3 - Mathematical Sciences Research Institute Publications

SP - 19

EP - 42

BT - Commutative Algebra and Noncommutative Algebraic Geometry

A2 - Eisenbud, David

A2 - Iyengar, Srikanth

A2 - Singh, Anurag

A2 - Stafford, Toby

A2 - Van den Bergh, Michel

PB - Cambridge University Press

CY - New York

ER -