Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of $F$-thresholds and related limits   The $F$-thresholds are important numerical invariants in prime
characteristic, whose existence had been established only under certain
assumptions. We show the existence of $F$-thresholds in full generality. We
study properties of standard graded algebras over a field for which $F$-pure
threshold and $F$-threshold at the irrelevant maximal ideal agree. We also
exhibit explicit bounds for the $a$-invariants and Castelnuovo-Mumford
regularity of Frobenius powers of ideals in terms of $F$-thresholds and
$F$-pure thresholds, obtaining existence of related limits in certain cases.

7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat