Timeline for sheafifying a projective limit of presheaves
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Jan 5, 2010 at 15:44 | comment | added | shenghao | That's an interesting example, but I hope (might be wrong) this phenomena won't happen "geometrically", i.e. for varieties over alg closed field k. | |
| Jan 5, 2010 at 5:17 | comment | added | Mariano Suárez-Álvarez | Completely changing an answer tends to be a bad idea... Writing a new one is usually best. | |
| Jan 5, 2010 at 4:48 | history | edited | Emerton | CC BY-SA 2.5 |
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| Jan 5, 2010 at 4:37 | comment | added | Emerton | I think this counts as a blunder. Let me know if you agree with the correction above. (Hopefully there won't be too many more iterations!) | |
| Jan 5, 2010 at 4:36 | history | edited | Emerton | CC BY-SA 2.5 |
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| Jan 5, 2010 at 4:08 | comment | added | shenghao | typo: "section" should be "second", as in "section exact sequence". | |
| Jan 5, 2010 at 4:06 | comment | added | shenghao | I have one more dumb question: it seems that the outer two maps being zero doesn't imply the inner map is also zero. Here's an "example": The first exact sequence is 0 -> Z -> Z^2 -> Z -> 0, where the first map sends a to (a,0) and the second sends (a,b) to b. The section exact sequence is similar, with Z replaced by Z/2Z. The middle map sends (a,b) to (b mod 2, 0), and the two outer maps are both zero. | |
| Jan 5, 2010 at 3:52 | vote | accept | shenghao | ||
| Jan 5, 2010 at 3:46 | history | edited | Emerton | CC BY-SA 2.5 |
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| Jan 5, 2010 at 3:40 | comment | added | Emerton | Yes, I assumed that $F$ is flat. The case $F = (F_1)$ is of course easier! I have edited the answer to take into account the non-flat case. | |
| Jan 5, 2010 at 3:38 | history | edited | Emerton | CC BY-SA 2.5 |
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| Jan 5, 2010 at 3:24 | comment | added | shenghao | Thanks! But why do we have that short exact sequence? I mean if F is not flat, it's only right exact. For instance F can be a constant system (F_1). | |
| Jan 5, 2010 at 3:06 | history | answered | Emerton | CC BY-SA 2.5 |