Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: "Geometric quotients are algebraic schemes" based on Fogarty's idea   Let S be a Noetherian scheme, f:X->Y a surjective S-morphism of S-schemes,
with X of finite type over S. We discuss what makes Y of finite type.
  First, we prove that if S is excellent, Y is reduced, and f is universally
open, then Y is of finite type. We apply this to understand Fogarty's theorem
in "Geometric quotients are algebraic schemes, Adv. Math. 48 (1983), 166--171"
for the special case that the group scheme G is flat over the Noetherian base
scheme S. Namely, we prove that if G is a flat S-group scheme of finite type
acting on X and f is its strict orbit space, then Y is of finite type.
  Utilizing the technique used there, we also prove that Y is of finite type if
f is flat. The same is true if S is excellent, f is proper, and Y is
Noetherian.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex