Vol. 200, No. 1, 2001

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Splitting fields of G-varieties

Zinovy Reichstein and Boris Youssin

Vol. 200 (2001), No. 1, 207–249
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 H1(K,G)H1(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.

Milestones
Received: 16 September 1999
Revised: 6 July 2000
Published: 1 September 2001
Authors
Zinovy Reichstein
Department of Mathematics
Oregon State University
Corvallis OR 97331
Boris Youssin
Department of Mathematics and Computer Science
University of the Negev
Be’er Sheva’
Israel
Hashofar 26/3
Ma’ale Adumim
Israel