Timeline for What is the Zariski topology good/bad for?
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16 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jul 31, 2010 at 18:56 | comment | added | Harry Gindi | @Ryan: That's definitely not true. A morphism of rings is etale if it is formally etale and finitely presented. It is formally etale if it has the unique LLP with respect to all quotients by a square-zero ideal. | |
| Jun 29, 2010 at 15:06 | comment | added | Ryan Reich | Let me tack on to BCnrd's answer the trivial statement that one cannot even talk about etale morphisms without having already developed a theory of algebraic geometry based on the Zariski topology. For example, the definition of etale mentions the Zariski local rings. | |
| Apr 18, 2010 at 1:36 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
corrected spelling
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| Apr 18, 2010 at 0:33 | answer | added | Kevin H. Lin | timeline score: 0 | |
| Apr 18, 2010 at 0:23 | answer | added | Sean Tilson | timeline score: 2 | |
| Apr 16, 2010 at 14:38 | history | edited | Qfwfq | CC BY-SA 2.5 |
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| Apr 16, 2010 at 13:28 | history | edited | Qfwfq | CC BY-SA 2.5 |
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| Apr 16, 2010 at 12:37 | answer | added | Donu Arapura | timeline score: 32 | |
| Apr 16, 2010 at 2:29 | answer | added | Emerton | timeline score: 32 | |
| Apr 16, 2010 at 1:07 | answer | added | Alicia Garcia-Raboso | timeline score: 9 | |
| Apr 15, 2010 at 23:51 | comment | added | Harry Gindi | Thanks for the clarification. I knew it sounded suspect. I think I read it on Wikipedia, which is never ever ever wrong ;). | |
| Apr 15, 2010 at 23:48 | comment | added | BCnrd | No way, not true. Zariski topology is useful for doing actual computations, constructing analytifications, formal schemes (for formal GAGA), open Bruhat cell, applications to commutative algebra, and so on. Proofs in etale cohomology use Zariski-stratifications. Useful to have actual space in which can make affine opens to do computations. Just look at the proofs of most serious theorems in etale sheaf theory. If one never reads proofs of hard theorems it may seem otherwise, but ignoring Zariski topology sounds bad. Each has its own uses. It's algebraic geometry. | |
| Apr 15, 2010 at 23:16 | comment | added | Harry Gindi | I heard somewhere (although I don't remember if it was a reputable source) that the étale topology is a wholesale replacement for the Zariski topology for pretty much every use. Could someone elaborate on whether or not this is even true? | |
| Apr 15, 2010 at 22:56 | answer | added | Kevin H. Lin | timeline score: 3 | |
| Apr 15, 2010 at 20:32 | history | asked | Qfwfq | CC BY-SA 2.5 |