Timeline for algebraic varieties whose fundamental group is subgroup separable wrt subvariety subgroups
Current License: CC BY-SA 3.0
4 events
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| Mar 24, 2014 at 5:41 | comment | added | mmm | Thanks, interesting! But I am more interested in positive examples. Are there any large classes of known examples that do have the property (that my theorem applies to), except for varieties with nilpotent fundamental groups? | |
| Mar 24, 2014 at 4:50 | comment | added | Ian Agol | There are examples of Deligne of lattices which are not residually finite (central extensions of $Sp(2n,\mathbb{Z})$). One might be able to find such an example which is a fundamental group of an algebraic variety, and such that the center is the fundamental group of a subvariety (so it wouldn't be separable). But this is speculation - I don't know how one would carry out such a construction. However, by analogy, I know that $\tilde{Sp(2,\mathbb{Z})}= B_3$ is the fundamental group of an algebraic variety (although this case is subgroup separable). mathoverflow.net/a/79283/1345 | |
| Mar 23, 2014 at 23:14 | comment | added | Misha | The trouble is that we know very little about such subgroups. For instance, product of surface groups is not LERF but I see no way to prove or disprove that images of fundamental groups of Riemann surfaces in it are separable. | |
| Mar 23, 2014 at 20:42 | history | asked | mmm | CC BY-SA 3.0 |