Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graded annihilators and uniformly $F$-compatible ideals   Let $R$ be a commutative (Noetherian) local ring of prime characteristic $p$
that is $F$-pure. This paper is concerned with comparison of three finite sets
of radical ideals of $R$, one of which is only defined in the case when $R$ is
$F$-finite (that is, is finitely generated when viewed as a module over itself
via the Frobenius homomorphism). Two of the afore-mentioned three sets have
links to tight closure, via test ideals. Among the aims of the paper are a
proof that two of the sets are equal, and a proposal for a generalization of I.
M. Aberbach's and F. Enescu's splitting prime.

6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph