Geodesic
Simple algebras and quadratic forms
Izvestiya. Mathematics, Tome 38 (1992) no. 1, pp. 215-221 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1992},
     volume = {38},
     number = {1},
     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
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
%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/

[1] Bass Kh., Algebraicheskaya $K$-teoriya, Mir, M., 1973 | MR | Zbl

[2] Manin Yu. I., “Lektsii o $K$-funktore v algebraicheskoi geometrii”, UMN, 23:5 (1969), 3–86 | MR

[3] Serr Zh.-P., Kogomologii Galua, Mir, M., 1968 | MR

[4] Khartskhorn R., Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[5] Kaplansky I., “Quadratic forms”, J. Math. Soc Japan, 5:2 (1953), 200–207 | MR | Zbl

[6] Lam T. Y., The algebraic theory of quadratic forms, Reading, Massachusetts, 1973 | MR | Zbl

[7] Merkurjev A. S., Suslin A. A., On the norm residue homomorphism of dergee three, Preprint E-9-96, LOMI, Leningrad, 1986 | MR

[8] Milnor J., “Algebraic $K$-theory and quadratic forms”, Invent. Math., 9:4 (1970), 318–344 | DOI | MR | Zbl

[9] Swan R. G., “$K$-theory of quadric hypersurfaces”, Ann. Math., 122:1 (1985), 113–154 | DOI | MR