Mathematics – Rings and Algebras
Scientific paper
2007-02-20
Mathematics
Rings and Algebras
13 pages
Scientific paper
The bounded derived category of coherent sheaves on a smooth projective variety is known to be equivalent to the triangulated category of perfect modules over a DG algebra. DG algebras, arising in this way, have to satisfy some compactness and smoothness conditions. In this paper, we describe a Serre functor on the category of perfect modules over an arbitrary compact and smooth DG algebra and use it to prove the existence of a non-degenerate pairing on the Hochschild homology of the DG algebra. This pairing is an algebraic analog of a well-known pairing on the Hodge cohomology of a smooth projective variety.
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