Timeline for On Ring Schemes
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2015 at 23:22 | answer | added | Qfwfq | timeline score: 1 | |
| Feb 17, 2012 at 9:10 | comment | added | Martin Brandenburg | @Scott: Thanks for this clarification. Where are ring schemes such as $\mathbf{O}^n$ treated in SGA3 (I cannot read ~ 1700 pages)? @Erin: I think this is offtopic. | |
| Feb 5, 2012 at 12:59 | comment | added | user10290 | You might to read Hans Schoutens notes from his class this semester: websupport1.citytech.cuny.edu/faculty/hschoutens/… He draws a connection between equivalent understandings of a direct limit of rings through ultra products and an algebraic definition involving stalks. | |
| Feb 5, 2012 at 7:20 | comment | added | S. Carnahan♦ | Martin's example is called $\mathbf{O}^n$ in SGA3. If we forget the multiplicative structure, the additive group scheme is called $\mathbf{G}_a^n$. In general, should avoid using the notation describing plain affine space when there is extra structure in play. | |
| Feb 4, 2012 at 17:42 | comment | added | Martin Brandenburg | $\mathbb{A}^n_S(T)=\mathcal{O}_T(T)^n$ is a ring for every scheme $T/S$. | |
| Feb 4, 2012 at 15:01 | vote | accept | RPC | ||
| Feb 4, 2012 at 12:52 | comment | added | Qfwfq | If the ring-schemes are not assumed to be commutative, there is a theory of (relative over $S$) Azumaya algebras. en.wikipedia.org/wiki/Azumaya_algebra | |
| Feb 4, 2012 at 12:49 | comment | added | Qfwfq | @Martin: which multiplication do you have in mind that would work for every $n$ ? | |
| Feb 4, 2012 at 9:58 | answer | added | A Stasinski | timeline score: 14 | |
| Feb 4, 2012 at 8:59 | comment | added | Martin Brandenburg | $\mathbb{A}^n_S$ is a ring scheme over $S$, or does this count as a non interesting example? | |
| Feb 4, 2012 at 8:50 | comment | added | Eric Peterson | I don't know what algebraic geometers have done, but there's a nontrivial amount of applicative algebraic topology literature about affine formal ring schemes / coalgebraic rings. Such objects appear when building the co/homology of the destabilization of another co/homology theory. Searching on any of 'Hopf ring', 'coalgebraic ring', 'biring', 'ring-ring', and potentially 'Tall-Wraith monoid' will probably turn topology-application type stuff up. | |
| Feb 4, 2012 at 6:51 | history | asked | RPC | CC BY-SA 3.0 |