Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On asymptotic depth of integral closure filtration and an application   Let $(A,\mathfrak{m})$ be an analytically unramified formally equidimensional
Noetherian local ring with $\ depth \ A \geq 2$. Let $I$ be an
$\mathfrak{m}$-primary ideal and set $I^*$ to be the integral closure of $I$.
Set $G^*(I) = \bigoplus_{n\geq 0} (I^n)^*/(I^{n+1})^*$ be the associated graded
ring of the integral closure filtration of $I$. We prove that $\ depth \
G^*(I^n) \geq 2$ for all $n \gg 0$. As an application we prove that if $A$ is
also an excellent normal domain containing an algebraically closed field
isomorphic to $A/\m$ then there exists $s_0$ such that for all $s \geq s_0$ and
$J$ is an integrally closed ideal \emph{strictly} containing
$(\mathfrak{m}^s)^*$ then we have a strict inequality $\mu(J) <
\mu((\mathfrak{m}^s)^*)$ (here $\mu(J)$ is the number of minimal generators of
$J$).

23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics