Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fonction asymptotique de Samuel des sections hyperplanes et
  multiplicit\'e   Let $(A,\mathfrak{m}_A,k)$ be a local noetherian ring and $I$ an
$\mathfrak{m}_A$-primary ideal. The asymptotic Samuel function (with respect to
$I$) $\bar{v}_I$ $:$ $A\longrightarrow \mathbb{R}\cup {+\infty}$ is defined by
$\bar{v}_I(x)=lim_{k \to \+infty}\frac{ord_I(x^k}{k}$, $\forall x \in A$.
Similary, one defines for another ideal $J$, $\bar{v}_I(J)$ as the minimum of
$\bar{v}_I(x)$ as $x$ varies in $J$. Of special interest is the rational number
$\bar{v}_I(\mathfrak{m}_A)$. We study the behavior of the Asymptotic Samuel
Function (with respect to $I$) when passing to hyperplanes sections of $A$ as
one does for the theory of mixed multiplicities.

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The categories of this paper are: hep-th
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an