Timeline for Monodromy with algebraic fundamental groups
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2010 at 17:10 | answer | added | Greg Kuperberg | timeline score: 3 | |
| Oct 24, 2010 at 15:02 | comment | added | algori | It is relatively rare for a bundle to have a section (then e.g. the long exact sequence of the homotopy groups splits etc). But the monodromy action exists for each locally trivial fiber bundle and more generally for a Serre bundle, since all one ever uses in the above definition is the covering homotopy property. More precisely, for a Serre bundle the action is defined up to homotopy, but for a locally trivial bundle with a connection say we get a genuine action by homeomorphisms. However, this action is seldom by algebraic maps: think e.g. of the universal level $N>2$ elliptic curve. | |
| Oct 23, 2010 at 21:42 | comment | added | Donu Arapura | I don't have time to write a full answer, but here a few comments (1) there is no way to capture the topological fundamental group in a purely algebraic fashion; the best you can hope for is some approximation. (2) For the etale fundamental group, see SGA1 exp X cor 1.4. Then you'll need to a work a bit from there to the analogue you want. | |
| Oct 23, 2010 at 21:25 | history | edited | Makhalan Duff | CC BY-SA 2.5 |
added 23 characters in body
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| Oct 23, 2010 at 21:10 | history | asked | Makhalan Duff | CC BY-SA 2.5 |