Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coleff-Herrera currents, duality, and Noetherian operators   Let $\I$ be a coherent subsheaf of a locally free sheaf $\Ok(E_0)$ and
suppose that $\F=\Ok(E_0)/\I$ has pure codimension. Starting with a residue
current $R$ obtained from a locally free resolution of $\F$ we construct a
vector-valued Coleff-Herrera current $\mu$ with support on the variety
associated to $\F$ such that $\phi$ is in $\I$ if and only if $\mu\phi=0$. Such
a current $\mu$ can also be derived algebraically from a fundamental theorem of
Roos about the bidualizing functor, and the relation between these two
approaches is discussed. By a construction due to Bj\"ork one gets Noetherian
operators for $\I$ from the current $\mu$. The current $R$ also provides an
explicit realization of the Dickenstein-Sessa decomposition and other related
canonical isomorphisms.

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The categories of this paper are: hep-ph
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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: bayes-an
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The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: q-bio