Timeline for An algebraic vector bundle is trivialized by open sets. How many does one need?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2010 at 13:22 | vote | accept | Georges Elencwajg | ||
| Dec 15, 2010 at 22:24 | comment | added | Qing Liu | @Angelo: thanks. I see my mistakes. | |
| Dec 15, 2010 at 21:53 | comment | added | Angelo | To Georges: thank you for your kind words, and congratulations on your impeccable Italian. | |
| Dec 15, 2010 at 21:52 | comment | added | Angelo | To Qing Liu: if the rank varies the statement is false, at least if you interpret "trivialize" as I do. For example, if the rank takes $m$ different values you need at least $m$ different open subsets, and this can also happen if the dimension of $X$ is zero. The problem in the proof arises from the statement that a projective module over a semi-local ring is free, which is false if the rank is not constant. | |
| Dec 15, 2010 at 21:06 | comment | added | Qing Liu | @Angelo: I don't see the problem with the rank varying. Your proof does not use the rank. | |
| Dec 15, 2010 at 20:47 | comment | added | Georges Elencwajg | Dear Angelo, thank you for this fast and perfect answer. Sono impressionato ma, conoscendoti, per nulla stupito! Mille grazie, Angelo. | |
| Dec 15, 2010 at 20:32 | history | edited | Angelo | CC BY-SA 2.5 |
added 130 characters in body
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| Dec 15, 2010 at 19:56 | history | answered | Angelo | CC BY-SA 2.5 |