JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (2): 23-30.doi: 10.6040/j.issn.1671-9352.0.2021.506

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Relative derived category with respect to a duality pair

LIU Yan-ping   

  1. College of Economics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2022-01-07

Abstract: The relative derived categories with respect to Gorenstein(L,A)-projective and Gorenstein(L,A)-injective modules are introduced, where(L,A)is a fixed complete duality pair. A triangle-equivalence and description of morphisms in such relative derived categories are given. We also discuss a generalized Tate cohomology and obtain Avramov-Martsinkovsky exact sequences.

Key words: duality pair, relative derived category, Tate cohomology, Avramov-Martsinkovsky exact sequence

CLC Number: 

  • O153.3
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