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On semi-infinite cohomology of finite-dimensional graded algebras

Published online by Cambridge University Press:  23 February 2010

Roman Bezrukavnikov
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email:
Leonid Positselski
Sector of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow 127994, Russia (email:
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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).

Research Article
Copyright © Foundation Compositio Mathematica 2010


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