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COHOMOLOGY OF TORSION AND COMPLETION OF N-COMPLEXES

  • Ma, Pengju (Department of Mathematics Northwest Normal University) ;
  • Yang, Xiaoyan (Department of Mathematics Northwest Normal University)
  • Received : 2021.05.24
  • Accepted : 2021.12.13
  • Published : 2022.03.01

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

Acknowledgement

The author would like to thank the referees for the valuable comments and suggestions in shaping the paper into its present form.

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