Timeline for Locally constant sheaves for the étale topology, lack of intuition about "étale-localness"
Current License: CC BY-SA 2.5
7 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Jan 18, 2011 at 19:32 | comment | added | Donu Arapura | Dear Harry, I meant my statement the way Tom interpreted it. As to how I feel about "local isomorphisms are...", I find it funnier than helpful. | |
| Jan 18, 2011 at 19:30 | comment | added | Tom Goodwillie | You can get to (1) by way of "this thing can be covered by objects U such that U is isomorphic to one of those things". You can get to (2) by the equally reasonable "there is one of those things T such that this thing is locally isomorphic to T" | |
| Jan 18, 2011 at 19:30 | comment | added | Tom Goodwillie | A different ambiguity in expressions containing "locally" has to do with the way that this word carries hidden quantifiers. When it is combined with another expression containing hidden quantifiers of its own, then there is a question of precedence. "This thing is locally isomorphic to one of those things" might mean (1) "this thing has a cover by objects U such that there is one of those things T such that U is isomorphic to T" or it might mean (2) "there is one of those things T such that this thing can has a cover by objects U isomorphic to T". | |
| Jan 18, 2011 at 19:12 | comment | added | Tom Goodwillie | Harry, Donu never used the expression "local isomorphism". He used the expression "locally isomorphic", which I take to mean "locally admitting an isomorphism" rather than "admitting a [perhaps globally defined map which is a] local isomorphism", although I admit that this sort of expression could be a trap for the unwary or the uninitiated. | |
| Jan 18, 2011 at 18:30 | comment | added | Harry Gindi | Dear Donu, how do you feel about the following statement: Local isomorphisms between sheaves are global isomorphisms? | |
| Jan 18, 2011 at 18:04 | history | answered | Donu Arapura | CC BY-SA 2.5 |