Abstract
Let \((K,\mathcal {O},k)\) be a p-modular system and assume k is algebraically closed. We show that if Λ is an \(\mathcal {O}\)-order in a separable K-algebra, then \(\text {Pic}_{\mathcal {O}}({\Lambda })\) 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 \(\mathcal {O}\).
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This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/M02525X/1].
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Presented by: Peter Littelmann
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Eisele, F. The Picard Group of an Order and Külshammer Reduction. Algebr Represent Theor 24, 505–518 (2021). https://doi.org/10.1007/s10468-020-09957-x
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DOI: https://doi.org/10.1007/s10468-020-09957-x