"Geometric quotients are algebraic schemes" based on Fogarty's idea
| dc.creator | Hashimoto, Mitsuyasu | |
| dc.date | 2003-03-12 | |
| dc.date | 2004-09-13 | |
| dc.date.accessioned | 2026-07-07T06:32:55Z | |
| dc.date.available | 2026-07-07T06:32:55Z | |
| dc.description | 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. | |
| dc.description | 10 pages, minor error corrections and change of numbering of theorems | |
| dc.identifier | https://arxiv.org/abs/math/0303134 | |
| dc.identifier | http://arxiv.org/abs/math/0303134 | |
| dc.identifier | J. Math. Kyoto Univ. 43 (4) (2003), 807-814 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99018 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13E15; 14L24 (Primary), 13C15 (Secondary) | |
| dc.title | "Geometric quotients are algebraic schemes" based on Fogarty's idea | |
| dc.type | text |