Poisson C∞-schemes
Abstract
We introduce Poisson C∞-rings and Poisson local C∞-ringed spaces. We show that the spectrum of a Poisson C∞-ring is an affine Poisson C∞-scheme. We then discuss applications that include singular symplectic and Poisson reductions, singular quasi-Poisson reduction, coisotropic reduction and Poisson-Dirac subschemes.
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