We classify the Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we prove Harada's conjecture for all these blocks, and we prove Broue's abelian defect group conjecture for 30 of the 34 determined equivalence classes of blocks.

中文翻译：

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具有 32 阶基本阿贝尔缺陷群的块的 Morita 等价类

我们对具有 32 阶基本阿贝尔缺陷群的块的 Morita 等价类，相对于具有特征为 2 的代数闭合残差域的完整离散评估环进行分类。因此，我们证明了所有这些块的 Harada 猜想，并且我们证明了 34 个确定的等价类块中的 30 个的 Broue 阿贝尔缺陷群猜想。