Timeline for When is an almost geometric quotient flat?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2016 at 11:39 | comment | added | Friedrich Knop | That $R^G$ is a direct summand of $R$ follows from complete reducibility. The projection $R\to R^G$ is sometimes called the Reynolds operator. The purity of the inclusion of a direct summand is considered "obvious" by Hochster-Roberts in section 6 of their famous paper "Rings of invariants [$\ldots$] are Cohen-Macaulay". | |
| Aug 11, 2016 at 1:01 | comment | added | Avi Steiner | Do you have a reference for this fact about direct summands? | |
| Aug 11, 2016 at 0:53 | comment | added | Friedrich Knop | The injection $R^G\hookrightarrow R$ is always pure since $R^G$ is a direct summand of $R$ as an $R^G$-module. So "pure injective" is no restriction at all, at least in characteristic zero. | |
| Aug 11, 2016 at 0:49 | comment | added | Avi Steiner | Do you know if there's anything known about the less restrictive condition that the inclusion of rings $R^G\to R$ is pure injective? | |
| Aug 11, 2016 at 0:46 | vote | accept | Avi Steiner | ||
| Aug 11, 2016 at 0:44 | history | answered | Friedrich Knop | CC BY-SA 3.0 |