Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential graded Lie algebras controlling infinitesimal deformations
  of coherent sheaves   We use the Thom-Whitney construction to show that infinitesimal deformations
of a coherent sheaf F are controlled by the differential graded Lie algebra of
global sections of an acyclic resolution of the sheaf End(E), where E is any
locally free resolution of F. In particular, one recovers the well known fact
that the tangent space to deformations of F is Ext^1(F,F), and obstructions are
contained in Ext^2(F,F).
  The main tool is the identification of the deformation functor associated
with the Thom-Whitney DGLA of a semicosimplicial DGLA whose cohomology is
concentrated in nonnegative degrees with a noncommutative Cech cohomology-type
functor.

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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph