Timeline for Why is the prime spectrum not useful in non-archimedean analytic geometry?
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| when toggle format | what | by | license | comment | |
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| May 6, 2010 at 9:54 | vote | accept | CommunityBot | moved from User.Id=5117 by developer User.Id=36770 | |
| Apr 20, 2010 at 7:02 | comment | added | user5117 | Dear Brian, thanks for your answer, which I would accept if I could. The point about non-uniqueness of extension for non-maximal ideals is clear. I guess what I didn't grasp yet is why it isn't still useful to consider the non-maximal prime ideals, even in spite of this defect; Emerton's answer below gives an indication of this. | |
| Apr 19, 2010 at 19:58 | answer | added | Emerton | timeline score: 9 | |
| Apr 19, 2010 at 19:14 | answer | added | Kevin Buzzard | timeline score: 13 | |
| Apr 19, 2010 at 18:11 | comment | added | BCnrd | Because MaxSpec has more geometric appeal. Residue fields at closed pts are finite extns, so unique abs. value: $|f(x)|$ makes sense for max'l $x$. Not obvious how to include generic pts, is it? That's the answer. At other primes there are many ways to complete the residue field. For Berkovich spaces, Spec shows up. As prime spectrum consists of "all" field-valued pts of a ring, Berkovich spec consists of "all" non-arch field valued pts of Banach alg. Just like the utility of classical varieties when studying schemes, MaxSpec theory is not a waste of time (and technically easier to digest). | |
| Apr 19, 2010 at 16:58 | history | asked | user5117 | CC BY-SA 2.5 |