Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Construction of schemes over $F_1$, and over idempotent semirings:
  towards tropical geometry
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph