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- W2093026633 startingPage "207" @default.
- W2093026633 abstract "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." @default.
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- W2093026633 date "2001-09-01" @default.
- W2093026633 modified "2023-10-18" @default.
- W2093026633 title "Splitting fields of G-varieties" @default.
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- W2093026633 doi "https://doi.org/10.2140/pjm.2001.200.207" @default.
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