Timeline for Does there exist a Riemann surface corresponding to every field extension? Any other hypothesis needed?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2010 at 6:09 | comment | added | Charles Siegel | @Scott, Ahh, I always forget finitely generated hypotheses, they're just completely internalized to me. I should be more careful. | |
| Jun 18, 2010 at 4:42 | comment | added | BCnrd | If $K/k$ is any extension of fields one can define the Riemann-Zariski space ${\rm{RZ}}(K/k)$ to consist of all valuations on $K$ trivial on $k$. It has a natural quasi-compact "Zariski topology". These were used by Zariski mainly for $K/k$ finitely generated, but make sense in general. Variants on this have been extremely useful in recent work in non-archimedean geometry as well as resolution of singularities (cf. work of M. Temkin). | |
| Jun 18, 2010 at 4:35 | comment | added | S. Carnahan♦ | The extension needs to be finitely generated, so you can avoid things like $\mathbb{C}(t,t^{1/2},t^{1/3},\ldots)$. | |
| Jun 18, 2010 at 4:16 | comment | added | H. Hasson | Chapter I, Section 1.6. | |
| Jun 18, 2010 at 4:08 | history | answered | Charles Siegel | CC BY-SA 2.5 |