论文标题
扭转和完成N-复合物的结合学
Cohomology of torsion and completion of N-complexes
论文作者
论文摘要
我们介绍了Koszul $ n $ -complex的概念，$ \ check {\ mathrm {c}} $ $ \ check {\ mathrm {c}} $ ech $ n $ - complex和望远镜$ n $ -complex。此外，我们在共同体上$ \ mathfrak {a} $ - 扭曲$ n $ complexes和共生学上$ \ mathfrak {a} $ - adic完整$ n $ - complexes的类别之间给出等效性$ \ otimes $ cohomology）和通过本地的共同体学（分别派生完成），所有这些都产生了相同的不变性。
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.
