Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completion and torsion over commutative DG rings   Let $\operatorname{CDG}_{cont}$ be the category whose objects are pairs
$(A,\bar{\mathfrak{a}})$, where $A$ is a commutative DG-algebra and
$\bar{\mathfrak{a}}\subseteq \mathrm{H}^0(A)$ is a finitely generated ideal,
and whose morphisms $f:(A,\bar{\mathfrak{a}}) \to (B,\bar{\mathfrak{b}})$ are
morphisms of DG-algebras $A \to B$, such that
$(\mathrm{H}^0(f)(\bar{\mathfrak{a}})) \subseteq \bar{\mathfrak{b}}$. Letting
$\mathrm{Ho}(\operatorname{CDG}_{cont})$ be its homotopy category, obtained by
inverting adic quasi-isomorphisms, we construct a functor
$\mathrm{L}\Lambda:\mathrm{Ho}(\operatorname{CDG}_{cont}) \to
\mathrm{Ho}(\operatorname{CDG}_{cont})$ which takes a pair
$(A,\bar{\mathfrak{a}})$ into its non-abelian derived $\bar{\mathfrak{a}}$-adic
completion. We show that this operation has, in a derived sense, the usual
properties of adic completion of commutative rings, and that if $A =
\mathrm{H}^0(A)$ is an ordinary noetherian ring, this operation coincides with
ordinary adic completion. As an application, following a question of Buchweitz
and Flenner, we show that if $\Bbbk$ is a commutative ring, and $A$ is a
commutative $\Bbbk$-algebra which is $\mathfrak{a}$-adically complete with
respect to a finitely generated ideal $\mathfrak{a}\subseteq A$, then the
derived Hochschild cohomology modules
$\operatorname{Ext}^n_{A\otimes^{\mathrm{L}}_{\Bbbk} A} (A,A)$ and the derived
complete Hochschild cohomology modules
$\operatorname{Ext}^n_{A\widehat{\otimes}^{\mathrm{L}}_{\Bbbk} A} (A,A)$
coincide, without assuming any finiteness or noetherian conditions on $\Bbbk,
A$ or on the map $\Bbbk \to A$.

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The categories of this paper are: stat
29
The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: hep-th