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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1992_38_1_a10,
     author = {A. S. Merkur'ev},
     title = {Simple algebras and quadratic forms},
     journal = {Izvestiya. Mathematics },
     pages = {215--221},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a10/}
}
TY  - JOUR
AU  - A. S. Merkur'ev
TI  - Simple algebras and quadratic forms
JO  - Izvestiya. Mathematics 
PY  - 1992
SP  - 215
EP  - 221
VL  - 38
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a10/
LA  - en
ID  - IM2_1992_38_1_a10
ER  - 
%0 Journal Article
%A A. S. Merkur'ev
%T Simple algebras and quadratic forms
%J Izvestiya. Mathematics 
%D 1992
%P 215-221
%V 38
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a10/
%G en
%F IM2_1992_38_1_a10
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/