Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zero-separating invariants for linear algebraic groups   Let $G$ be a linear algebraic group over a field $k$, and let $V$ be a
$G$-module. Recall that the nullcone of $(G,V)$ is the set of points $v$ in $V$
with the property that $f(v)=0$ for every positive degree homogeneous invariant
$f$ in $k[V]^G$. We define numbers $\delta(G,V)$ and $\sigma(G,V)$ associated
with a given representation as follows: $\delta(G,V)$ is the smallest number
$d$ such that, for any point $v$ in $V^G$ outside the nullcone, there exists an
invariant $f$ of degree at most $d$ such that $f(v)$ is not zero; $\sigma(G,V)$
is the same thing with $V^G$ replaced by $V$. If k has positive characteristic,
we show that $\delta(G,V)$ is infinite for all subgroups of $GL_2(k)$
containing a unipotent subgroup, and that $\sigma(G,V)$ is finite if and only
if $G$ is finite. If $k$ has characteristic zero we show that $\delta(G,V)=1$
for all linear algebraic groups and that if $\sigma(G,V)$ is finite then the
connected component of $G$ is unipotent.

31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org