This work concerns finite free complexes over commutative noetherian rings, in particular over group algebras of elementary abelian groups. The main contribution is the construction of complexes such that the total rank of their underlying free modules, or the total length of their homology, is less than predicted by various conjectures in the theory of transformation groups and in local algebra.

中文翻译：

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小秩小同调的有限自由复形的例子

这项工作涉及可交换诺特环上的有限自由复形，特别是基本阿贝尔群的群代数。主要贡献是构建复合体，使得它们的潜在自由模块的总秩或它们的同源性的总长度小于变换群理论和局部代数中的各种猜想所预测的。