Timeline for The "pullback presheaf" and the proper base change theorem in topology
Current License: CC BY-SA 3.0
9 events
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| Aug 22, 2011 at 17:39 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Aug 18, 2011 at 22:08 | comment | added | Benjamin Steinberg | In my opinion, the pullback sheaf is easiest to understand using the etale space formulation of sheaves rather than the functorial description. If $Z\rightarrow Y$ is etale, then the pullback $X\times_Y Z\rightarrow X$ is etale over X. | |
| Aug 18, 2011 at 19:11 | comment | added | Hugo Chapdelaine | @Angelo, thanks for your very simple and instructive example! | |
| Aug 18, 2011 at 19:04 | comment | added | Hugo Chapdelaine | I needed my map $f$ to be a closed embedding and not just proper. | |
| Aug 18, 2011 at 19:01 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
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| Aug 18, 2011 at 18:59 | comment | added | Hugo Chapdelaine | Hi @Angelo, thanks for pointing my mistake, I know what is wrong! | |
| Aug 18, 2011 at 18:52 | comment | added | Peter McNamara | Greg Muller provides an exmaple in mathoverflow.net/questions/45212/… | |
| Aug 18, 2011 at 18:30 | comment | added | Angelo | Take $Y$ to be a point, $X$ a non-empty Hausdorff space that is not a point, and $\mathcal F$ a non-zero sheaf: then $f'\mathcal F$ is not sheaf. This would also seem to give counterexamples to your statement, unless I misunderstand something. | |
| Aug 18, 2011 at 18:07 | history | asked | Hugo Chapdelaine | CC BY-SA 3.0 |