Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
复制标题
多诺万猜想，具有阿贝尔缺陷群和离散估值环的块
DOI：
10.1007/s00209-019-02354-1
复制
发表时间：
2019
影响因子：
0.8
通讯作者：
Eaton C
中科院分区：
文献类型：
--
作者：
Eaton C
我们给出了一个约化拟单群的多诺万猜想块与阿贝尔亏损群定义的一个适当的离散赋值环。其后果是，多诺万的猜想持有块与阿贝尔缺陷群的素数两个，而且，使用最近的工作法雷尔和凯萨，为任意素数多诺万的猜想块与阿贝尔缺陷群减少到边界的嘉当不变量块quasisimple群体的缺陷。一个结果的独立利益是，在一般情况下（即为任意缺陷组）多诺万的猜想块是一个后果的预测界限的弗罗贝纽斯数和嘉当不变量，证明了凯萨块定义在代数封闭领域。
We give a reduction to quasisimple groups for Donovan’s conjecture for blocks with abelian defect groups defined with respect to a suitable discrete valuation ring. Consequences are that Donovan’s conjecture holds for-blocks with abelian defect groups for the prime two, and that, using recent work of Farrell and Kessar, for arbitrary primes Donovan’s conjecture for-blocks with abelian defect groups reduces to bounding the Cartan invariants of blocks of quasisimple groups in terms of the defect. A result of independent interest is that in general (i.e. for arbitrary defect groups) Donovan’s conjecture for-blocks is a consequence of conjectures predicting bounds on the-Frobenius number and on the Cartan invariants, as was proved by Kessar for blocks defined over an algebraically closed field.