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Derived Quot schemes

I. Ciocan-Fontanine·M. Kapranov
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Abstract

Realizing a part of the Derived Deformation Theory program, we construct a "derived" analog of the Grothendieck's Quot scheme parametrizing subsheaves in a given coherent sheaf F on a smooth projective variety X. This analog is a differential graded manifold RQuot_h(F) (so it is always smooth in an appropriate sense) whose tangent space at a point represented by a subsheaf K in F, is a cochain complex quasiisomorphic to RHom(K, F/K).

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I. Ciocan-Fontanine, M. Kapranov. 2000-05-16. Derived Quot schemes. https://arxiv.org/abs/math/9905174

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