# The quantization conjecture revisited

@article{Teleman1998TheQC, title={The quantization conjecture revisited}, author={Constantin Teleman}, journal={Annals of Mathematics}, year={1998}, volume={152}, pages={1-43} }

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X, L), the cohomologies of L over the GIT quotient X//G equal the invariant part of the cohomologies over X. This generalizes the theorem of [GS] on global sections, and strengthens its subsequent extensions ([JK], [li]) to RiemannRoch numbers. Remarkable by-products are the invariance of cohomology of vector bundles over X//G under a small… Expand

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