Splendid Equivalences: Derived Categories and Permutation Modules
Splendid Equivalences: Derived Categories and Permutation Modules
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DOI：
10.1112/plms/s3-72.2.331
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发表时间：
1996-03
影响因子：
1.8
通讯作者：
J. Rickard
中科院分区：
文献类型：
--
作者：
J. Rickard
我们介绍了一个辉煌的有限群块之间的等价的概念，这是一个加强的概念，等价的派生类别。这样的等价总是由双侧倾斜复形引起的，其项是置换模的和，这一特征与以下信念相容：在有限域上的约化群的情况下，这些复形应该与Deligne-Lusztig变体的/-adic上同调有关。我们表明，一个辉煌的等价具有良好的后果以上，从派生等价遵循。特别是，它给出了，对于主块，一个结构上的解释Brou^的概念的一个同型（一个兼容的家庭完美的等距）。我们给出了几个例子，包括森田等价的例子，是辉煌的一个意想不到的非平凡的方式。
We introduce the notion of a splendid equivalence between blocks of finite groups, which is a strengthening of the notion of an equivalence of derived categories. Such an equivalence is always induced by a two-sided tilting complex whose terms are summands of permutation modules, a feature that is compatible with the belief that these complexes should be related to the /-adic cohomology of Deligne-Lusztig varities in the case of reductive groups over finite fields. We show that a splendid equivalence has good consequences over and above those that follow from a derived equivalence. In particular, it gives, for principal blocks, a structural explanation of Brou^'s concept of an isotypy (a compatible family of perfect isometries). We give several examples, including examples of Morita equivalences that are splendid in an unexpectedly non-trivial way.