Timeline for global sections of some sheaves

Current License: CC BY-SA 2.5

12 events

when toggle format	what		by	license	comment
Mar 1, 2011 at 21:32	history	edited	J.C. Ottem	CC BY-SA 2.5	added 16 characters in body
Mar 1, 2011 at 20:38	comment	added	Sándor Kovács		@t3suji: my apologies. It's funny with these comments. Since we can't edit them, they become out of place after the answer gets edited...
Mar 1, 2011 at 19:46	comment	added	J.C. Ottem		I edited the answer above to make it more precise. Thanks to t3suji and Sandor for their comments.
Mar 1, 2011 at 19:23	history	edited	J.C. Ottem	CC BY-SA 2.5	added 267 characters in body
Mar 1, 2011 at 18:55	comment	added	t3suji		@Sandor Kovacs. Of course it is true that 1) and 2) are equivalent. I was objecting to the original answer (which has been edited away): the idea was to get 2) from connectivity and then derive 1).
Mar 1, 2011 at 17:55	comment	added	Sándor Kovács		ps: In other words, the nilpotents would have to show up in $\Gamma(Y,\mathcal{I}^r/\mathcal{I}^{r+1})$ for some $r$.
Mar 1, 2011 at 17:54	comment	added	Sándor Kovács		@t3suji: JC is saying that $\Gamma(Y,\mathcal{O}_X/\mathcal{I}^{r+1})$ injects into $\Gamma(Y,\mathcal{O}_X/\mathcal{I}^{r})$ for all $r$, so by iterating this you get that $\Gamma(Y,\mathcal{O}_X/\mathcal{I}^{r})$ injects into $\Gamma(Y,\mathcal{O}_X/\mathcal{I})$. There are no nilpotents there.
Mar 1, 2011 at 17:52	history	edited	Sándor Kovács	CC BY-SA 2.5	corrected typo
Mar 1, 2011 at 17:29	history	edited	J.C. Ottem	CC BY-SA 2.5	deleted 71 characters in body
Mar 1, 2011 at 14:13	comment	added	t3suji		Sorry, but how do you know $rY$ has no global functions? Connectivity does not imply this, because the scheme is non-reduced, so it may have global nilpotent functions.
Mar 1, 2011 at 11:12	history	edited	J.C. Ottem	CC BY-SA 2.5	added 133 characters in body; added 6 characters in body
Mar 1, 2011 at 11:04	history	answered	J.C. Ottem	CC BY-SA 2.5