Timeline for Morphisms of locally ringed spaces into affine schemes
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2016 at 14:15 | comment | added | Jérôme Poineau | See stacks.math.columbia.edu/tag/01I1. | |
| Sep 23, 2016 at 13:46 | comment | added | Dylan Wilson | See also the elusive EGA I.1.8 which is found in... EGA II at the end as an addendum, which is freely available online. :) | |
| Sep 23, 2016 at 11:51 | vote | accept | Arrow | ||
| Sep 23, 2016 at 11:43 | answer | added | HeinrichD | timeline score: 6 | |
| Jan 11, 2016 at 13:35 | comment | added | Jason Starr | Injectivity of the map follows from the characterization of the diagonal in $Y\times Y$ as the zero scheme of the kernel of the multiplication morphism $R\otimes R \to R$. For surjectivity, first you construct the set map $f:X\to Y$ by sending $p\in X$ to the kernel of $R\to \Gamma(X,\mathcal{O}_X) \to \kappa(p)$, then you check that $f^{-1}(D(r))$ is open for each $r\in R$, and finally you define $f^\#:\mathcal{O}_Y \to f_*\mathcal{O}_X$ to be the unique morphism of sheaves of algebras compatible with $\widetilde{R} \to \widetilde{\Gamma(X,\mathcal{O}_X)}$ on $Y$. | |
| Jan 11, 2016 at 13:34 | comment | added | Arrow | @abx widely available as it may be, I don't have access to it and I haven't been able to find it online. Also, will the downvoter explain the downvote? | |
| Jan 11, 2016 at 13:30 | comment | added | abx | The 1971 edition is in Springer Grundlehren series, which is widely available. | |
| Jan 11, 2016 at 12:19 | history | asked | Arrow | CC BY-SA 3.0 |