Timeline for Finite dimensional division algebra over pseudo-algebraic closed field
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 24, 2017 at 17:00 | vote | accept | user43198 | ||
| Aug 24, 2017 at 13:10 | comment | added | Dirk | No. As mentioned in the answer, finite fields are $C_1$, and every extension field of them is such an algebra with itself (so not the base field) as center. | |
| Aug 24, 2017 at 12:55 | comment | added | Matthias Wendt | @user43198: yes, if you consider division algebras whose center is the given field, then these things are classified by the Brauer group, and the Brauer group is trivial for PAC fields. | |
| Aug 24, 2017 at 12:53 | comment | added | user43198 | It seems from the proof of Proposition $6.2.3$, page $171$ of "Central simple algebras and Galois cohomology" by Gille and Szamuely, that this is true for $C_1$-fields. But I am not an expert. | |
| Aug 24, 2017 at 12:42 | history | answered | Dirk | CC BY-SA 3.0 |