Corestrictions of algebras and splitting fields
| dc.creator | Krashen, Daniel | |
| dc.date | 2007-04-25 | |
| dc.date.accessioned | 2026-07-07T07:58:19Z | |
| dc.date.available | 2026-07-07T07:58:19Z | |
| dc.description | Given a field $F$, an étale extension $L/F$ and an Azumaya algebra $A/L$, one knows that there are extensions $E/F$ such that $A \otimes_F E$ is a split algebra over $L \otimes_F E$. In this paper we bound the degree of a minimal splitting field of this type from above and show that our bound is sharp in certain situations, even in the case where $L/F$ is a split extension. This gives in particular a number of generalizations of the classical fact that when the tensor product of two quaternion algebras is not a division algebra, the two quaternion algebras must share a common quadratic splitting field. In another direction, our constructions combined with results of Karpenko also show that for any odd prime number $p$, the generic algebra of index $p^n$, and exponent $p$ cannot be expressed nontrivially as the corestriction of an algebra over any extension field if $n < p^2$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0704.3443 | |
| dc.identifier | http://arxiv.org/abs/0704.3443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127962 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16K20 | |
| dc.title | Corestrictions of algebras and splitting fields | |
| dc.type | text |