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Donovan’s conjecture, crossed products and algebraic group actions

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Abstract

Donovan’s conjecture, on blocks of finite group algebras over an algebraically closed field of prime characteristicp, asserts that for any finitep-groupD, there are only finitely many Morita equivalence classes of blocks with defect groupD. The main result of this paper is a reduction theorem: It suffices to prove the conjecture for groups generated by conjugates ofD. A number of other finiteness results are proved along the way. The main tool is a result on actions of algebraic groups.

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Germany

    Burkhard Külshammer

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  1. Burkhard Külshammer
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Correspondence to Burkhard Külshammer.

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Külshammer, B. Donovan’s conjecture, crossed products and algebraic group actions. Israel J. Math. 92, 295–306 (1995). https://doi.org/10.1007/BF02762084

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  • DOI: https://doi.org/10.1007/BF02762084

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