Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic cyclic homology as sheaf cohomology   We study a noncommutative version of the infinitesimal site of Grothendieck.
A theorem of Grothendieck establishes that the cohomology of the structure
sheaf on the infinitesimal topology of a scheme of characteristic zero is de
Rham cohomology. We prove that, for the noncommutative infinitesimal topology
of an associative algebra over a field of characteristic zero, the cohomology
of the structure sheaf modulo commutators is periodic cyclic cohomology. We
also compute the noncommutative infinitesimal cohomology of other sheaves. For
example we show that hypercohomology with coefficients in $K$-theory gives the
fiber of the Jones-Goodwillie character which goes from $K$-theory to negative
cyclic homology.

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The categories of this paper are: quant-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: stat
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org