Mathematics – Algebraic Geometry
Scientific paper
2005-04-28
Mathematics
Algebraic Geometry
Latex 2e, 39 pages. Added a dedication (to J. Bernstein)
Scientific paper
We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves on $X$ is equivalent to the dervied category of finitely generated left modules over a non-commutative algebra $R$, a non-commutative resolution of $Y$ in a sense close to that of M. Van den Bergh. We also prove some applications, such as: two resolutions are derived-equivalent; every resolution $X$ admits a "resolution of the diagonal"; the cohomology groups of the fibers of the map $X \to Y$ are spanned by fundamental classes of algebraic cycles.
No associations
LandOfFree
Derived equivalences by quantization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Derived equivalences by quantization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Derived equivalences by quantization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-402665