Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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
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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.

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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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