Abstract We reformulate the problem of bounding the total rank of the homology of perfect chain complexes over the group ring F p [ G ] of an elementary abelian p-group G in terms of commutative algebra. This extends results of Carlsson for p = 2 to all primes. As an intermediate step, we construct an embedding of the derived category of perfect chain complexes over F p [ G ] into the derived category of p-DG modules over a polynomial ring.

中文翻译：

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自由 (Z/p)n 复合体和 p-DG 模块

摘要 我们根据交换代数重新表述了在基本阿贝尔 p 群 G 的群环 F p [ G ] 上的完美链络合物同调的总秩的边界问题。这将卡尔森对 p = 2 的结果扩展到所有素数。作为中间步骤，我们将 F p [ G ] 上的完美链复合体的派生类别嵌入到多项式环上的 p-DG 模块的派生类别中。