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2 results

  • On semi-infinite cohomology of finite-dimensional graded algebras

  • Part of
  • Roman Bezrukavnikov, Leonid Positselski
  • Journal:
    Compositio Mathematica / Volume 146 / Issue 2 / March 2010
    Published online by Cambridge University Press:
    23 February 2010, pp. 480-496
    Print publication:
    March 2010
    • Article
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  • We describe a general setting for the definition of semi-infinite cohomology of finite-dimensional graded algebras, and provide an interpretation of such cohomology in terms of derived categories. We apply this interpretation to compute semi-infinite cohomology of some modules over the small quantum group at a root of unity, generalizing an earlier result of Arkhipov (posed as a conjecture by B. Feigin).

  • APPLICATIONS OF COTORSION PAIRS

  • HENNING KRAUSE, ØYVIND SOLBERG
  • Journal:
    Journal of the London Mathematical Society / Volume 68 / Issue 3 / December 2003
    Published online by Cambridge University Press:
    17 November 2003, pp. 631-650
    Print publication:
    December 2003

  • For an artin algebra $\Lambda$, cotorsion pairs are studied for the category ${\rm mod}\Lambda$ of finitely presented $\Lambda$-modules and for the category ${\rm Mod}\Lambda$ of all $\Lambda$-modules. It is shown that every cotorsion pair for ${\rm mod}\Lambda$ induces a cotorsion pair for ${\rm Mod}\Lambda$. This has some interesting applications, even for the category of finitely presented modules. Another theme of the paper is the interplay between cotorsion and torsion pairs. This leads to a conjecture which is an analogue of the telescope conjecture in stable homotopy theory.