Cohomology of torsion and completion of N-complexes

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 D N (R) of N-complexes using the Čech N-complex and the telescope N-complex. Moreover, we give an equivalence between the category of cohomologically a-torsion N-complexes and the category of cohomologically aadic 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.