Geodesic
Supersingular $K3$ surfaces over fields of characteristic 2
Izvestiya. Mathematics, Tome 13 (1979) no. 1, pp. 147-165 
A. N. Rudakov; I. R. Shafarevich. Supersingular $K3$ surfaces over fields of characteristic 2. Izvestiya. Mathematics, Tome 13 (1979) no. 1, pp. 147-165. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the unirationality of supersingular $K3$ surfaces over a field of characteristic 2 is proved and a classification of such surfaces is given. Bibliography: 14 titles.

[1] Artin M., “Supersingular $K3$ surfaces”, Ann. Scient. Ecole Norm. Sup., 7:4 (1974), 543–568 | MR

[2] Bombieri E., Mumford D., “Enriques's clasification of surfaces in char. III”, Invent. math., 35 (1976), 197–232 | DOI | MR | Zbl

[3] Bourbaki N., Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, 1337, Hermann, Paris, 1968 | MR

[4] Dolgachev I. V., Parshin A. N., “Differenta i diskriminant regulyarnykh otobrazhenii”, Matem. zametki, 4:5 (1968), 519–523

[5] Kneser M., “Klassenzahlen definiter quadratischer Formen”, Arch. der Math., VIII:4 (1957), 241–249 | DOI | MR

[6] Kodaira K., “On compact complex analytic surfaces. I”, Ann. Math., 71 (1960), 111–152 | DOI | MR | Zbl

[7] O'Meara, The arithmetic theory of quadratic forms, New York, 1950

[8] Nèron A., “Modéles minimaux des varietés abéliennes sur les corps locaux”, Publ. Math. IHES, no. 2, 1–125

[9] Ogg A., “Elliptic curves and wild ramification”, Amer. J. Math., 89:1 (1967), 530–572 | DOI | MR

[10] Pyatetskii-Shapiro I. I., Shafarevich I. R., “Teorema Torelli dlya algebraicheskikh poverkhnostei tipa $K3$”, Izv. AN SSSR. Ser. matem., 35 (1971), 530–572

[11] Rudakov A. N., Shafarevich I. R., “Neseparabelnye morfizmy algebraicheskikh poverkhnostei”, Izv. AN SSSR. Ser. matem., 40:6 (1976), 1269–1307 | MR | Zbl

[12] Rudakov A. N., Shafarevich I. R., “O kvaziellipticheskikh poverkhnostyakh tipa $K3$”, Uspekhi matem. nauk, 33:1 (1978), 227–228 | MR | Zbl

[13] Serre J.-P., Cours d'Arithmetique, Paris, 1970

[14] Tate J., Courbes elliptiques: formulaire. Modular functions of one variable. IV, Lecture Notes in Math., 476 | Zbl