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Stratifying integral representations of finite groups

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 نشر من قبل Tobias Barthel
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Tobias Barthel




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We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case established in celebrated work of Benson, Iyengar, and Krause. Further consequences include a verification of the generalized telescope conjecture in this context, a tensor product formula for integral cohomological support, as well as a generalization of Quillens stratification theorem for group cohomology. Our proof makes use of novel descent techniques for stratification in tensor-triangular geometry that are of independent interest.



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