Timeline for Why is there no "regular etale fundamental group"?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2012 at 22:53 | vote | accept | James D. Taylor | ||
| Oct 4, 2012 at 18:45 | comment | added | Manish Kumar | The simplest reason is that there many regular covers whose Galois closure is not regular. For example $\Q(t^{1/4})/\Q(t)$. | |
| Oct 4, 2012 at 18:32 | comment | added | Angelo | Just take the fiber product of a regular cover with itself. The correct "relative" substitute for the fundamental group of X is Deligne's relative fundamental groupoid, as defined in “Le Groupe Fondamental de la Droite Projective Moins Trois Points” math.ias.edu/files/deligne/GaloisGroups.pdf. | |
| Oct 4, 2012 at 18:04 | answer | added | David E Speyer | timeline score: 11 | |
| Oct 4, 2012 at 17:16 | comment | added | David Loeffler | Is it fanciful to think of this as being a bit like the non-existence of a maximal totally ramified extension of a local field? | |
| Oct 4, 2012 at 16:19 | comment | added | James D. Taylor | unknown, it sounds like you have an example in mind. | |
| Oct 4, 2012 at 16:17 | comment | added | John Pardon | Surely the answer is going to be that fiber products takes you out of your category of "regular" covers. | |
| Oct 4, 2012 at 16:03 | history | asked | James D. Taylor | CC BY-SA 3.0 |