Geodesic
Rational intersection points of two hyperquadrics
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 631-642 
A. A. Bel'skii. Rational intersection points of two hyperquadrics. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 631-642. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article equivalence relations are studied on the set of rational intersection points of two hyperquadrics of sufficiently general type, the classes of which form in a natural way an abelian group of period two. For elliptic curves the constructions performed agree with the known ones. Bibliography: 9 titles.

[1] Algebraicheskie poverkhnosti, Trudy Matem. in-ta im. V. A. Steklova, 75, 1965 | MR | Zbl

[2] Algebraicheskaya teoriya chisel, Mir, Moskva, 1970

[3] A. Grothendieck, “Le groupe de Brauer”, Sem. Bourbaki, 290 (1965); 297, 1965–1966 | Zbl

[4] Dzh. Kassels, “Diofantovy uravneniya so spetsialnym rassmotreniem ellipticheskikh krivykh”, Matematika, 12:1 (1968), 113–160

[5] Yu. I. Manin, “Kubicheskie giperpoverkhnosti. I”, Kvazigruppy klassov tochek, Izv AN SSSR, seriya matem., 32 (1968), 1223–1244 | MR | Zbl

[6] Yu. I. Manin, “Kubicheskie giperpoverkhnosti. III. Lupy Mufang i ekvivalentnost Brauera”, Matem. sb., 79(121) (1959), 155–170 | MR

[7] Yu. I. Manin, Ratsionalnye poverkhnosti nad sovershennymi polyami, Publ. Math. IHES, no. 30, 1966 | MR

[8] V. Khodzh, D. Pido, Metody algebraicheskoi geometrii, t. II, IL, Moskva, 1954

[9] N. G. Chebotarev, Teoriya algebraicheskikh funktsii, Gostekhizdat, Moskva–Leningrad, 1948