Geodesic
Simple algebras and quadratic forms
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 215-221.

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This paper gives a criterion for the splittability of a central simple finitedimensional division algebra under the extension of the ground field to the universal splitting field of a certain quadratic form. The criterion is stated in terms of the Clifford algebra of the quadratic form. As a corollary, it is shown that the $u$-invariant of a field can take any even values. 
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A. S. Merkur'ev. Simple algebras and quadratic forms. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 215-221. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a10/

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