@article {Izhboldin:March 1999:1386-923X:19,
	author = "Izhboldin O.T.",
	author = "Karpenko N.A.",
	title = "Generic Splitting Fields of Central Simple Algebras: Galois Cohomology and Nonexcellence",
	journal = "Algebras and Representation Theory",
	volume = "2",
	year = "March 1999",
	abstract = "<P>A field extension L / F is called excellent if, for any quadratic form <IMG SRC="/iso-ents/isogrk32/phi-s.gif" ALT="phis"> over F, the anisotropic part (<IMG SRC="/iso-ents/isogrk32/phi-s.gif" ALT="phis">L)an of <IMG SRC="/iso-ents/isogrk32/phi-s.gif" ALT="phis"> over L is defined over F; L / F is called universally excellent if L <IMG SRC="/iso-ents/isoamsb/sdot.gif" ALT="sdot"> E / E is excellent for any field extension E / F. We study the excellence property for a generic splitting field of a central simple F-algebra. In particular, we show that it is universally excellent if and only if the Schur index of the algebra is not divisible by 4. We begin by studying the torsion in the second Chow group of products of Severi&#150;Brauer varieties and its relationship with the relative Galois cohomology group H3(L / F) for a generic (common) splitting field L of the corresponding central simple F-algebras.</P>",
	pages = "19-59(41)",
	url = "http://www.ingentaconnect.com/content/klu/alge/1999/00000002/00000001/00194907"
}