Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative
  Tori   The first part of these notes gives an introduction to noncommutative
projective geometry after Artin--Zhang. The second part provides an overview of
the work of Polishchuk that reconciles noncommutative two-tori having real
multiplication with the Artin--Zhang setting.

30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph