Timeline for What is the transcendence degree of Q_p and C over Q?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2010 at 17:19 | comment | added | Georges Elencwajg | Very nice, Pete: +1. Bourbaki gives a formula analogous to your max formula for the cardinality of L (in his first exercise for §14, Chap.V of Algebra), only it is false for finite fields [which you wisely excluded] ! How do you downvote him ? :-) | |
| Feb 16, 2010 at 5:28 | comment | added | Pete L. Clark | @basic: Your "actual" question is actually interesting. More generally, one can ask whether a field $K$ is a "nontrivial function field", i.e., whether there exists a subfield $F$ of $K$ such that $K/F$ is finitely generated and tr. deg. of $K/F$ is positive and finite. I believe such a field must be "Hilbertian", which rules out $Q_p$. | |
| Feb 16, 2010 at 5:20 | comment | added | natura | Thank you. It's really clear when one considers the cardinality...Actually I was wondering if Q_p could be the function field of some variety besides Spec(Q_p) or Spec(Z_p), as some kind of analogy of fields of tr.deg 1 corresponds to curves. I don't know if it's a "right" question though... | |
| Feb 16, 2010 at 5:15 | history | edited | Pete L. Clark | CC BY-SA 2.5 |
added 418 characters in body; deleted 15 characters in body
|
| Feb 16, 2010 at 5:13 | vote | accept | natura | ||
| Feb 16, 2010 at 5:08 | history | answered | Pete L. Clark | CC BY-SA 2.5 |