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- W2085465518 abstract "Let $X$ be an irreducible algebraic variety defined over a field $k$, let $mathcal {R}$ be a sheaf of (noncommutative) noetherian $k$-algebras on $X$ containing the sheaf of regular functions $mathcal {O}$ and let $R$ be the ring of global sections. We show that under quite reasonable abstract hypotheses (concerning the existence of a faithfully flat overring of $R$ obtained from the local sections of $mathcal {R}$) there is an equivalence between the category of $R$-modules and the category of sheaves of $mathcal {R}$-modules which are quasicoherent as $mathcal {O}$-modules. This shows that the equivalence of categories established by Beilinson and Bernstein as the first step in their proof of the KazhdanLusztig conjectures (where $R$ is a primitive factor ring of the enveloping algebra of a complex semisimple Lie algebra, and $mathcal {R}$ is a sheaf of twisted differential operators on a generalised flag variety) is valid for more fundamental reasons than is apparent from their work." @default.
- W2085465518 created "2016-06-24" @default.
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- W2085465518 date "1985-03-01" @default.
- W2085465518 modified "2023-09-26" @default.
- W2085465518 title "Sheaves of noncommutative algebras and the Beilinson-Bernstein equivalence of categories" @default.
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- W2085465518 doi "https://doi.org/10.1090/s0002-9939-1985-0773985-3" @default.
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