The Picard Group of an Order and Külshammer Reduction

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Abstract

Let (K, O, k) be a p-modular system and assume k is algebraically closed. We show that if Λ is an O-order in a separable K-algebra, then Pic O(Λ) carries the structure of an algebraic group over k. As an application to the modular representation theory of finite groups, we show that a reduction theorem by Külshammer concerned with Donovan’s conjecture remains valid over O.

Original languageEnglish
Pages (from-to)505-518
Number of pages14
JournalAlgebras and Representation Theory
Volume24
Issue number2
Early online date16 Mar 2020
DOIs
Publication statusPublished - Apr 2021

Keywords

  • Finite groups
  • Modular Representation theory
  • Orders
  • Representation theory

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