Timeline for Families of abelian varieties on the line (or more generally simply connected varieties)
Current License: CC BY-SA 3.0
12 events
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| May 2, 2016 at 14:10 | answer | added | Ariyan Javanpeykar | timeline score: 3 | |
| May 2, 2016 at 8:42 | comment | added | Ariyan Javanpeykar | @PiotrAchinger The isotriviality of families of ordinary abelian varieties is also proven in Moret-Bailly's 1985 asterisque 129 "Pinceaux de varietes abeliennes" in Thm. 5.1 (see also Thm. 5.2) on page 237 Chapter XI. Note that Moret-Bailly attributes Thm. 5.1 to Raynaud. I guess the paper of Nori-Srinivas came out at the same time. | |
| Apr 30, 2016 at 7:24 | comment | added | Piotr Achinger | NB I heard you like Serre-Tate, so you might appreciate this little fact as well: Nori and Srinivas in "Varieties in positive characteristic with trivial tangent bundle" prove that in characteristic p, every family of ordinary abelian varieties over a smooth projective curve becomes trivial after a finite etale cover. In particular, every family of ordinary abelian varieties over a proper variety (no assumptions on $\pi_1$) is isotrivial. | |
| Apr 29, 2016 at 21:47 | comment | added | Piotr Achinger | J. Kollár, "Shafarevich maps and automorphic forms", MR1341589 ams.org/mathscinet-getitem?mr=1341589 | |
| Apr 29, 2016 at 20:19 | vote | accept | Alex Youcis | ||
| Apr 29, 2016 at 17:04 | answer | added | Donu Arapura | timeline score: 5 | |
| Apr 29, 2016 at 17:01 | history | edited | Alex Youcis | CC BY-SA 3.0 |
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| Apr 29, 2016 at 16:59 | comment | added | Alex Youcis | @PiotrAchinger Hey Piotr! Thanks, I'll look into this. I'm having trouble locating the original paper. Do you have a clue what the title is? Thanks! | |
| Apr 29, 2016 at 16:52 | answer | added | ACL | timeline score: 6 | |
| Apr 29, 2016 at 16:26 | history | edited | Alex Youcis | CC BY-SA 3.0 |
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| Apr 29, 2016 at 15:47 | comment | added | Piotr Achinger | There is a notion, introduced I think by Kollar, of "large fundamental group". A variety has large $\pi_1$ if the image of the $\pi_1$ of every subvariety is infinite. He states a conjecture (attributed to Shafarevich) that a variety has large (topological) fundamental group iff the universal cover is a Stein space. I think that this conjecture should imply (modulo stacky issues) that the answer to Q1 (and maybe Q2, by looking at the corresponding period domain) is affirmative. | |
| Apr 29, 2016 at 15:38 | history | asked | Alex Youcis | CC BY-SA 3.0 |