Timeline for A local global principle over function fields
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2016 at 6:27 | comment | added | Arne Smeets | Maybe ultraproducts can help? Haven't thought this through, just guessing. | |
| Oct 4, 2016 at 11:04 | comment | added | Jason Starr | Actually, now I see that there are some isotrivial families of Fermat hypersurfaces such that for all but finitely many $p$, the restriction of the family over $\overline{\mathbb{F}_p}(t)$ has no rational sections, even though they are inseparably rationally connected. This is one reason that inseparable rational connectedness is quite different from separable rational connectedness. | |
| Oct 4, 2016 at 9:23 | comment | added | Jason Starr | I would have thought one could produce counterexamples by considering isotrivial families of Fermat surfaces of large degree in $\mathbb{P}^3$. By Shioda, the reductions modulo infinitely many primes $p$ are (inseparably) rationally connected fibrations over a curve, but the degree $M$ of the unirational parameterization grows with $M$. | |
| Oct 4, 2016 at 9:00 | history | asked | Felipe Voloch | CC BY-SA 3.0 |