Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: De Rham and infinitesimal cohomology in Kapranov's model for
  noncommutative algebraic geometry   The title refers to the nilcommutative or $NC$-schemes introduced by M.
Kapranov in math.AG/9802041. The latter are noncommutative nilpotent
thickenings of commutative schemes. We consider also the parallel theory of
nil-Poisson or $NP$-schemes, which are nilpotent thickenings of commutative
schemes in the category of Poisson schemes. We study several variants of de
Rham cohomology for $NC$- and $NP$-schemes. The variants include nilcommutative
and nil-Poisson versions of the de Rham complex as well as of the cohomology of
the infinitesimal site introduced by Grothendieck. It turns out that each of
these noncommutative variants admits a kind of Hodge decomposition which allows
one to express the cohomology groups of a noncommutative scheme $Y$ as a sum of
copies of the usual (de Rham, infinitesimal) cohomology groups of the
underlying commutative scheme $X$ (Theorems 6.2, 6.5, 6.8). As a byproduct we
obtain new proofs for classical results of Grothendieck (Corollary 6.3) and of
Feigin-Tsygan (Corollary 6.9) on the relation between de Rham and infinitesimal
cohomology and between the latter and periodic cyclic homology.

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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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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: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: comp-gas