Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ueber die Tiefe von Invariantenringen unendlicher Gruppen   Let K be an algebraically closed field. For a graded K-Algebra R, we write
cmdef R:=dim R -depth R. We show that for each reductive group G (over K) which
is not linearly reductive, there exists a faithful G-module V such that cmdef
K[\sum_i=1^k V]^G >= k-2 for all k. We will give such a V explicitly.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg