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1 results

  • 16 - Derived Torsion over NC Graded Rings

  • Amnon Yekutieli, Ben-Gurion University of the Negev, Israel
  • Book:
    Derived Categories
    Published online:
    15 November 2019
    Print publication:
    19 December 2019, pp 462-507

  • Summary

    Let A be a connected graded ring over the base field K, with augmentation ideal m. In this chapter we study derived m-torsion, both for complexes of graded A-modules and for complexes of graded bimodules. The graded bimodule A* := HomK(A,K) is graded-injective and m-torsion on both sides. One of the main results is on the representability of the right derived m-torsion functor RΓm. Under quite general conditions the functor RΓm is isomorphic to the left derived tensor functor P⊗LA(-), where P := RΓm(A). We also prove the NC MGM Equivalence in the connected graded context and a theorem on symmetric derived m-torsion. The χ condition of Artin and Zhang is introduced in Section 16.5. We study how this condition interacts with symmetric derived m-torsion.