Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the length function of saturations of ideal powers   For an ideal $I$ in a local ring $(R, \fm)$, we prove that the integer-valued
function $\ell_R(H^0_\fm(R/I^{n+1}))$ is a polynomial for $n$ big enough if
either $I$ is a principle ideal or $I$ is generated by part of an almost
p-standard system of parameters. Furthermore, we are able to compute the
coefficients of this polynomial in terms of length of certain local cohomology
modules and usual multiplicity if either the ideal is principal or it is
generated by part of a standard system of parameters in a generalized
Cohen-Macaulay ring. We also give an example of an ideal generated by part of a
(general) system of parameters such that the function
$\ell_R(H^0_\fm(R/I^{n+1}))$ is not a polynomial for $n\gg 0$.

1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg