Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From geometric to function-theoretic Langlands (or how to invent
  shtukas)   This is an informal note that explains that the classical Langlands theory
over function fields can be obtained from the geometric one by taking the trace
of Frobenius. The operation of taking the trace of Frobenius takes place at the
categorical level, and this we deduce that the space of automorphic functions
is the trace of the Frobenius on the category of automorphic sheaves.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc