arXiv 2212.092372022-12math.CTmath.RT

稳定 Hom 函子的有限表示、Bass 挠与余挠余根

The finite presentation of the stable Hom functors, the Bass torsion, and the cotorsion coradical

Alex Martsinkovsky

备注：: The previous version has been split into two separate papers. Section 4 has been augmented by additional results on linear control systems and made into a separate article entitled "The defect, the Malgrange functor, and linear control systems". The new Section 4 deals with sub-stabilization of the tensor product and with related functors. A new application of the defect has been added

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AI总结：

本文研究稳定 Hom 函子及张量积次稳定化的有限表示条件，揭示其亏格与 Bass 挠、余挠的联系，并给出意外应用。

摘要：

我们给出了稳定 Hom 函子具有有限表示的充分和/或必要条件。当协变 Hom 函子模去投射对象后具有有限表示时，其亏格同构于固定参数的 Bass 挠。当逆变 Hom 函子模去内射对象后具有有限表示时，其亏格同构于固定参数的余挠。我们还给出了张量积的次稳定化具有有限表示的充分条件。张量积的有限表示引出了一个意想不到的应用。

英文摘要：

We provide necessary and/or sufficient conditions for the stable Hom functors to be finitely presented. When the covariant Hom functor modulo projectives is finitely presented, its defect is isomorphic to the Bass torsion of the fixed argument. When the contravariant Hom functor modulo injectives is finitely presented, its defect is isomorphic to the cotorsion of the fixed argument. We also give a sufficient condition for the sub-stabilization of the tensor product to be finitely presented. A finite presentation of the tensor product leads to an unexpected application.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。