Algebroid prestacks and deformations of ringed spaces

Lowen, Wendy

doi:10.1090/S0002-9947-07-04354-1

Algebroid prestacks and deformations of ringed spaces
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Trans. Amer. Math. Soc. 360 (2008), 1631-1660 Request permission

Abstract:

For a ringed space $(X,\mathcal {O})$, we show that the deformations of the abelian category $\mathsf {Mod}(\mathcal {O})$ of sheaves of $\mathcal {O}$-modules (Lowen and Van den Bergh, 2006) are obtained from algebroid prestacks, as introduced by Kontsevich. In case $X$ is a quasi-compact separated scheme the same is true for $\mathsf {Qch}(\mathcal {O})$, the category of quasi-coherent sheaves on $X$. It follows in particular that there is a deformation equivalence between $\mathsf {Mod}(\mathcal {O})$ and $\mathsf {Qch}(\mathcal {O})$.

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