Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant total ring of fractions and factoriality of rings generated
  by semiinvariants   Let $F$ be an affine flat group scheme over a commutative ring $R$, and $S$
an $F$-algebra (an $R$-algebra on which $F$ acts). We define an equivariant
analogue $Q_F(S)$ of the total ring of fractions $Q(S)$ of $S$. It is the
largest $F$-algebra $T$ such that $S\subset T\subset Q(S)$, and $S$ is an
$F$-subalgebra of $T$. We study some basic properties.
  Utilizing this machinery, we give some new criteria for factoriality (UFD
property) of (semi-)invariant subrings under the action of algebraic groups,
generalizing a result of Popov. We also prove some variations of classical
results on factoriality of (semi-)invariant subrings. Some results over an
algebraically closed base field are generalized to those over an arbitrary base
field.

21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas