## 2009.33: Modular representations of profinite groups

2009.33:
J.W. MacQuarrie
(2009)
*Modular representations of profinite groups.*

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## Abstract

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra of a profinite group, where the underlying field is a finite field of characteristic p.

We define the concept of relative projectivity for such a module. We prove a characterization of finitely generated relatively projective modules analogous to the finite case with additions of interest to the profinite theory. We introduce vertices and sources for indecomposable finitely generated modules over the completed group algebra and show that the expected conjugacy properties hold - for sources this requires additional assumptions. Finally we prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | modular representation theory, profinite group, virtually pro-p group, relative projectivity, vertex, source, Green's indecomposability theorem, coinvariant |

Subjects: | MSC 2000 > 16 Associative rings and algebras MSC 2000 > 20 Group theory and generalizations MSC 2000 > 22 Topological groups, Lie groups |

MIMS number: | 2009.33 |

Deposited By: | Dr J.W. MacQuarrie |

Deposited On: | 03 May 2009 |

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