Supersingular curves of genus two and class numbers
Compositio Mathematica, Tome 57 (1986) no. 2, pp. 127-152. 
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     author = {Ibukiyama, Tomoyoshi and Katsura, Toshiyuki and Oort, Frans},
     title = {Supersingular curves of genus two and class numbers},
     journal = {Compositio Mathematica},
     pages = {127--152},
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     volume = {57},
     number = {2},
     year = {1986},
     mrnumber = {827350},
     zbl = {0589.14028},
     language = {en},
     url = {http://www.numdam.org/item/CM_1986__57_2_127_0/}
}
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Ibukiyama, Tomoyoshi; Katsura, Toshiyuki; Oort, Frans. Supersingular curves of genus two and class numbers. Compositio Mathematica, Tome 57 (1986) no. 2, pp. 127-152. http://www.numdam.org/item/CM_1986__57_2_127_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] M. Eichler: Über die Idealklassenzahl hyperkomplexer Systeme. Math. Z. 43 (1938) 481-494. | JFM | MR | Zbl

[4] M. Eichler: Zur Zahlentheorie der Quaternionen-Algebren. J. Reine Angew. Math. 195 (1955) 127-151. | MR | Zbl

[5] K. Hashimoto: Class numbers of positive definite ternary quaternion hermitian forms. Proceed. Japan Acad. 59 Ser. A (1983) 490-493. | MR | Zbl

[6] K. Hashimoto and T. Ibukiyama: On 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,(III) ibid. to appear. | MR | Zbl

[7] T. Hayashida: A class number associated with the product of an elliptic curve with itself. J. Math. Soc. Japan 20 (1968) 26-43. | MR | Zbl

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

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

[10] T. Katsura and F. Oort: Families of supersingular abelian surfaces. In preparation. | Numdam | Zbl

[11] N. Koblitz: P-adic variation of the zeta-function over families defined over finite fields. Compositio Math. 31 (1975) 119-218. | Numdam | MR | Zbl

[12] S. Lang: Abelian Varieties. New York: Interscience-Wiley (1959). | MR | Zbl

[13] Yu. I. Manin: The theory of commutative formal groups over fields of finite characteristic. Russian Math. Surveys 18 (1963) 1-83. | MR | Zbl

[14] D. Mumford: Abelian Varieties. Oxford University Press (1970). | MR | Zbl

[15] P. Norman and F. Oort: Moduli of abelian varieties. Ann. of Math. 112 (1980) 413-439. | MR | Zbl

[16] N.O. Nygaard: Slopes of powers of frobenius on crystalline cohomology. Ann. Sci. Ecole Norm. Sup. 14 (1981) 369-401. | Numdam | MR | Zbl

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

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

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

[20] T. Shioda: Some results on unirationality of algebraic surfaces. Math. Ann. 230 (1977) 153-168. | MR | Zbl

[21] T. Shioda: Supersingular K3 surfaces. Lecture Notes in Math. 732. Berlin- Heidelberg-New York: Springer (1979) 564-591. | MR | Zbl

[22] W.C. Waterhouse: Abelian varieties over finite fields. Ann. Sci. Ecole Norm. Sup. 2 (1962) 521-560. | Numdam | MR | Zbl

[23] N. Yui: On the Jacobian varieties of hyperelliptic curves over fields of characteristic p > 2. Journ. of Alg. 52 (1978) 378-410. | MR | Zbl