Splitting fields of G-varieties
| dc.creator | Reichstein, Zinovy | |
| dc.creator | Youssin, Boris | |
| dc.date | 1999-10-06 | |
| dc.date | 1999-10-21 | |
| dc.date.accessioned | 2026-07-07T05:31:04Z | |
| dc.date.available | 2026-07-07T05:31:04Z | |
| dc.description | Let $G$ be an algebraic group, $X$ a generically free $G$-variety, and $K=k(X)^G$. A field extension $L$ of $K$ is called a splitting field of $X$ if the image of the class of $X$ under the natural map $H^1(K, G) \mapsto H^1(L, G)$ is trivial. If $L/K$ is a (finite) Galois extension then $\Gal(L/K)$ is called a splitting group of $X$. We prove a lower bound on the size of a splitting field of $X$ in terms of fixed points of nontoral abelian subgroups of $G$. A similar result holds for splitting groups. We give a number of applications, including a new construction of noncrossed product division algebras. | |
| dc.description | In this revision we simplified the proof of Lemma 4.3. AMS LaTeX 1.1, 36 pages. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html | |
| dc.identifier | https://arxiv.org/abs/math/9910034 | |
| dc.identifier | http://arxiv.org/abs/math/9910034 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79211 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Splitting fields of G-varieties | |
| dc.type | text |