Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Essential p-dimension of algebraic tori   The essential dimension is a numerical invariant of an algebraic group G
which may be thought of as a measure of complexity of G-torsors over fields. A
recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the
essential dimension of a finite p-group. We obtain similar formulas for the
essential p-dimension of a broader class of groups, which includes all
algebraic tori.

7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con