Families of supersingular abelian surfaces
Compositio Mathematica, Volume 62 (1987) no. 2, pp. 107-167.
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Katsura, Toshiyuki; Oort, Frans. Families of supersingular abelian surfaces. Compositio Mathematica, Volume 62 (1987) no. 2, pp. 107-167. http://archive.numdam.org/item/CM_1987__62_2_107_0/

1 M. Deuring: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Univ. Hamburg 14 (1941) 197-272. | JFM | MR | Zbl

2 M. Eichler: Über die Idealklassenzahl total definiter Quaternionenalgebren. Math. Z. 43 (1938) 102-109. | JFM | MR | Zbl

3 T. Ekedahl: On supersingular curves and abelian varieties. Prépublications Univ. de Paris-Sud, Orsay (1985).

4 K. Hashimoto and T. Ibukiyama: On the class numbers of positive definite binary quaternion hermitian forms (I). J. Fac. Sci. Univ. Tokyo sect. IA, 27 (1980), 549-601(II) ibid. 28 (1981) 695-699. | MR | Zbl

5 T. Ibukiyama, T. Katsura and F. Oort: Supersingular curves of genus two and class numbers. Comp. Math. 57 (1986) 127-152. | Numdam | MR | Zbl

6 J. Igusa: Class number of a definite quaternion with prime discriminant. Proc. Nat. Acad. Sci. U.S.A. 44 (1958) 312-314. | MR | Zbl

7 J. Igusa: Arithmetic variety of moduli for genus two. Ann. of Math. 72 (1960) 612-649. | MR | Zbl

8 T. Katsura and F. Oort: Supersingular abelian varieties of dimension two or three and class numbers. To appear in Advanced Studies in Pure Math. | MR | Zbl

9 N. Koblitz: p-adic variation of the zeta-function over families defined over finite fields. Comp. Math. 31 (1975) 119-218. | Numdam | MR | Zbl

10 L. Moret-Bailly: Polarizations de degré 4 sur les surfaces abéliennes. C.R. Acad. Sci. Paris 289 (1979) 787-790. | MR | Zbl

11 L. Moret-Bailly: Familles de courbes et de variétés abéliennes sur P1. Astérisque 86 (1981) 109-140. | Zbl

12 D. Mumford: Abelian varieties. Oxford Univ. Press (1970). | MR | Zbl

13 D. Mumford and J. Fogarty: Geometric invariant theory (second enlarged edition). Berlin-Heidelberg- New York: Springer-Verlag (1982). | MR | Zbl

14 M.N. Narasimhan and M.V. Nori: Polarizations on an abelian variety. Geometry and analysis, Indian Acad. Sci. Bangalore (1980) 125-128. | Zbl

15 F. Oort: Subvarieties of moduli spaces. Invent. Math. 24 (1974) 95-119. | MR | Zbl

16 F. Oort: Which abelian surfaces are products of elliptic curves? Math. Ann. 214 (1975) 35-47. | MR | Zbl

17 H. Pinkham: Singularités de Klein, I. In Séminaire sur les singularités des surfaces. Lecture Notes in Math. 777, pp. 1-9. Berlin- Heidelberg-New York: Springer-Verlag (1980). | Numdam | MR | Zbl

18 G. Shimura: Arithmetic of alternating forms and quaternion hermitian forms. J. Math. Soc. Japan 15 (1963) 33-65. | MR | Zbl

19 T. Shioda: Supersingular K3 surfaces. Lecture Notes in Math. 732, pp. 564-591. Berlin- Heidelberg-New York: Springer-Verlag (1979). | MR | Zbl

20 W.C. Waterhouse: Abelian varieties over finite fields. Ann. Sci. Éc. Norm. Sup. 4e série, t.2 (1969) 521-560. | Numdam | MR | Zbl

21 A. Weil: Zum Beweis des Torellischen Satzes. Nachr. Acad. Wiss. Göttingen Math. Phys. K1 (1957) 33-53. | MR | Zbl