挠的上同调与N-复形的完备化
Cohomology of torsion and completion of N-complexes
摘要：
本文利用$\check{\mathrm{C}}$ ech $N$-复形和望远镜$N$ -复形，在$N$-复形的导出范畴$\mathbf{D}_N(R)$中引入了Koszul $N$ -复形、$\check{\mathrm{C}}$ ech $N$ -复形和望远镜$N$ -复形的概念，以及显式导出挠和导出完备函子.此外，我们给出了上同调$\mathfrak{a}$ -挠$N$ -复形范畴与上同调$\mathfrak{a}$ -adic完全$N$ -复形范畴之间的等价性，并证明了在交换诺特环上，通过Koszul上同调，通过RHom上同调（分别为. $\otimes$上同调）和通过局部上同调（分别所有的不变量都是相同的。
英文摘要：
We introduce the notions of Koszul $N$-complex, $\check{\mathrm{C}}$ech $N$-complex and telescope $N$-complex, explicit derived torsion and derived completion functors in the derived category $\mathbf{D}_N(R)$ of $N$-complexes using the $\check{\mathrm{C}}$ech $N$-complex and the telescope $N$-complex. Moreover, we give an equivalence between the category of cohomologically $\mathfrak{a}$-torsion $N$-complexes and the category of cohomologically $\mathfrak{a}$-adic complete $N$-complexes, and prove that over a commutative noetherian ring, via Koszul cohomology, via RHom cohomology (resp. $\otimes$ cohomology) and via local cohomology (resp. derived completion), all yield the same invariant.
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。
