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The Picard group of an order and Külshammer reduction

Eisele, F. ORCID: 0000-0001-8267-2094 (2020). The Picard group of an order and Külshammer reduction. .


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 PicO(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 Kulshammer concerned with Donovan’s conjecture remains valid over O.

Publication Type: Monograph (Working Paper)
Additional Information: ©the authors, 2020.
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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