Timeline for Does there exist a Riemann surface corresponding to every field extension? Any other hypothesis needed?
Current License: CC BY-SA 2.5
7 events
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Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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Feb 24, 2012 at 13:19 | answer | added | stjc | timeline score: 0 | |
Jun 18, 2010 at 13:01 | vote | accept | Abhishek Parab | ||
Jun 18, 2010 at 11:22 | comment | added | Pete L. Clark | There are good answers below, but briefly: the "Zariski Riemann surface" is usually not a Riemann surface (sorry!): it is a top. space. When $K/k$ is f.g. of trdeg $1$, the Z.R.S. is essentially the Zariski topology on the unique complete, normal curve over $k$ with function field $K$. (When $k = \mathbb{C}$, there really is a compact Riemann surface here. Otherwise not.) If the trdeg is greater than one, the Z.R.S. is more complicated than any one variety with the given function field: it is keeping track of all models at once. If tr.deg. is zero, the Z.R.S. is a single point. | |
Jun 18, 2010 at 5:13 | answer | added | Tom Goodwillie | timeline score: 13 | |
Jun 18, 2010 at 4:08 | answer | added | Charles Siegel | timeline score: 2 | |
Jun 18, 2010 at 3:38 | history | asked | Abhishek Parab | CC BY-SA 2.5 |