Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric symmetric powers in the motivic homotopy category   Symmetric powers of quasi-projective schemes can be extended, in terms of
left Kan extensions, to geometric symmetric powers of motivic spaces. In this
paper, we study geometric symmetric powers and compare with various symmetric
powers in the unstable and stable motivic homotopy category of schemes over a
field.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con