Timeline for Exceptional specializations of Galois groups in the Hilbert Irreducibility Theorem
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 17, 2015 at 23:03 | vote | accept | 352506 | ||
| Dec 17, 2015 at 21:01 | comment | added | Joe Silverman | @352506 I think that one could take the proof described in Serre's Lectures on the Mordell-Weil Theorem and make it explicit, but offhand I don't know a reference where it is done. Hmmm... And that might just be for the $t$ such that $f(x,t)$ becomes reducible. Did you try searching on Google for "Effective Hilbert Irreducibility Theorem"? Among the top entries was the following, which likely has what you want: Effective Hilbert irreducibility, Erich Kaltofen, Information and Control, Volume 66, Issue 3, September 1985, Pages 123-137. | |
| Dec 17, 2015 at 20:41 | comment | added | 352506 | Where could I find a proof of the existence of such curves $C_i$ and maps $\phi_i$? | |
| Dec 17, 2015 at 19:19 | history | answered | Joe Silverman | CC BY-SA 3.0 |