Self-equivalences of stable module categories
Self-equivalences of stable module categories
复制标题
稳定模块类别的自等价性
DOI：
10.1007/pl00004789
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发表时间：
2000
影响因子：
0.8
通讯作者：
R. Rouquier
中科院分区：
文献类型：
--
作者：
J. Carlson;R. Rouquier
抽象的。设P是交换p-群，E是循环群，
自由作用在特征代数闭域P和k上的p '-群
$p>0$。在这篇文章中，我们证明了，
$k[P\rtimes E]$来自导出范畴的自等价
$k[P\rtimes E]$. Puig和Rickard的工作使我们能够推导出，如果具有缺陷群P和惯性商E的块B是Rickard等价于
$k[P\rtimes E]$，则它们是极好的里卡德等价。也就是说，Broué的原始猜想意味着Rickard在这种情况下对猜想的改进。所有这一切都来自于平凡模生成的厚子范畴的自等价的一般结果。
Abstract. Let P be an abelian p-group, E a cyclic
$p'$-group acting freely on P and k an algebraically closed field of characteristic
$p>0$. In this work, we prove that every self-equivalence of the stable module category of
$k[P\rtimes E]$ comes from a self-equivalence of the derived category of
$k[P\rtimes E]$. Work of Puig and Rickard allows us to deduce that if a block B with defect group P and inertial quotient E is Rickard equivalent to
$k[P\rtimes E]$, then they are splendidly Rickard equivalent. That is, Broué's original conjecture implies Rickard's refinement of the conjecture in this case. All of this follows from a general result concerning the self-equivalences of the thick subcategory generated by the trivial module.