Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the $\ell$-torsion in class groups   We prove for each integer $\ell\geq 1$ an unconditional upper bound for the
size of the $\ell$-torsion subgroup $Cl_K[\ell]$ of the class group of $K$,
which holds for all but a zero density set of number fields $K$ of degree
$d\in\{4,5\}$ (with the additional restriction in the case $d = 4$ that the
field be non-$D_4$). For sufficiently large $\ell$ this improves recent results
of Ellenberg, Matchett Wood, and Pierce, and is also stronger than the best
currently known pointwise bounds under GRH. Conditional on GRH and on a weak
conjecture on the distribution of number fields our bounds also hold for
arbitrary degrees $d$.

14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph