Kashiwara's D-affinity conjecture for formal quantizations

Let π:XS[[h]]\pi:{\mathfrak X}\to S[[h]] and the quantization sheaf Oh\operatorname{\cal O}_h satisfy the assumptions of Theorem~. Consider the global sections functor

Shv(X,Oh)Shv(S[[h]],πOh)\operatorname{Shv}({\mathfrak X},\operatorname{\cal O}_h)\longrightarrow\operatorname{Shv}(S[[h]],\pi_*\operatorname{\cal O}_h)

from sheaves of finitely generated Oh\operatorname{\cal O}_h-modules to sheaves of finitely generated πOh\pi_*\operatorname{\cal O}_h-modules on S[[h]]=S×^SpecK[[h]]S[[h]]=S\widehat{\times}\operatorname{Spec}K[[h]]. Kashiwara's conjecture. This functor is an equivalence of abelian categories over a dense open subset US[[h]]U\subset S[[h]].

The conjecture aims to generalize the D-affinity phenomenon from partial flag varieties to formal geometric quantizations. The precise assumptions of Theorem~ are not supplied here, and the source gives no resolution.

Sources & referencesView supporting material

Primary source

D. Kaledin, “Geometry and topology of symplectic resolutions”, arXiv:math/0608143 (2008).

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