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http://dx.doi.org/10.4134/JKMS.j210349

COHOMOLOGY OF TORSION AND COMPLETION OF N-COMPLEXES  

Ma, Pengju (Department of Mathematics Northwest Normal University)
Yang, Xiaoyan (Department of Mathematics Northwest Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.2, 2022 , pp. 379-405 More about this Journal
Abstract
We introduce the notions of Koszul N-complex, Čech N-complex and telescope N-complex, explicit derived torsion and derived completion functors in the derived category DN (R) of N-complexes using the Čech N-complex and the telescope N-complex. Moreover, we give an equivalence between the categories of cohomologically 𝖆-torsion N-complexes and cohomologically 𝖆-adic complete N-complexes, and prove that over a commutative Noetherian ring, via Koszul cohomology, via RHom cohomology (resp. ⊗ cohomology) and via local cohomology (resp. derived completion), all yield the same invariant.
Keywords
Koszul N-complex; telescope N-complex; torsion; completion;
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