On the field of definition of superspecial polarized abelian varieties and type numbers
Ibukiyama, Tomoyoshi ; Katsura, Toshiyuki
Compositio Mathematica, Tome 94 (1994), p. 37-46 / Harvested from Numdam
Publié le : 1994-01-01
@article{CM_1994__91_1_37_0,
     author = {Ibukiyama, Tomoyoshi and Katsura, Toshiyuki},
     title = {On the field of definition of superspecial polarized abelian varieties and type numbers},
     journal = {Compositio Mathematica},
     volume = {94},
     year = {1994},
     pages = {37-46},
     mrnumber = {1273924},
     zbl = {0817.14024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1994__91_1_37_0}
}
Ibukiyama, Tomoyoshi; Katsura, Toshiyuki. On the field of definition of superspecial polarized abelian varieties and type numbers. Compositio Mathematica, Tome 94 (1994) pp. 37-46. http://gdmltest.u-ga.fr/item/CM_1994__91_1_37_0/

1 Asai, T., The class number of positive definite quadratic forms, Japanese J. Math., 3 (1977) 239-296. | MR 529280 | Zbl 0376.10017

2 Deuring, M., Die Anzahl der Typen von Maximalordnungen einer definiten Quatemionenalgebra mit primer Grundzahl, Jahresberich Deutschen Math., 54 (1951) 24-41. | MR 36777 | Zbl 0039.02902

3 Deuring, M., Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941) 197-272. | JFM 67.0107.01 | MR 5125 | Zbl 0025.02003

4 Eichler, M., Uber die Idealklassenzahl total definiter quaternionen algebren, Math. Z., 43 (1938) 102-109. | JFM 63.0093.02 | MR 1545717 | Zbl 0017.15003

5 Hartshorne, R., Algebraic Geometry, Springer, New York, Berlin, Heidelberg, 1977. | MR 463157 | Zbl 0367.14001

6 Hashimoto, K., On Brandt matrices associated with the positive definite quaternion hermitian forms, J. Fac. Sci. Univ. Tokyo Sect. IA, 27 (1980) 227-245. | MR 573338 | Zbl 0433.10017

7 Hashimoto, K. and Ibukiyama, T., On class numbers of positive definite binary quaternion harmitian forms. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 27 (1980) 549-601. | MR 603952 | Zbl 0452.10029

8 Ibukiyama, T., On automorphism groups of positive definite binary quaternion hermitian lattices and new mass formula, pp. 301-349, Advanced Studies in Pure Math. Vol. 15, Kinokuniya, Tokyo, 1989. | MR 1040612 | Zbl 0703.11019

9 Ibukiyama, T., On rational points of curves of genus three over finite fields, to appear in Tohoku Math. J. | Zbl 0819.14007

10 Ibukiyama, T., Katsura, T. and Oort, F., Supersingular curves of genus two and class numbers, Compositio Math., 57 (1986) 127-152. | Numdam | MR 827350 | Zbl 0589.14028

11 Katsura, T. and Oort, F., Families of supersingular abelian surfaces, Compositio Math., 62 (1987) 107-167. | Numdam | MR 898731 | Zbl 0636.14017

12 Mumford, D., Abelian Varieties, Oxford University Press, 1970. | MR 282985 | Zbl 0223.14022

13 Serre, J.-P., A letter to Hashimoto and Ibukiyama, 1984.

14 Shimura, G., Arithmetic of alternating forms and quaternion hermitian forms, J. Math. Soc. Japan, 15 (1963) 33-65. | MR 146172 | Zbl 0121.28102

15 Shimura, G. and Taniyama, Y., Complex Multiplication of Abelian Varieties and its Applications to Number Theory, Publ. Math. Soc. Japan 6, 1961. | MR 125113 | Zbl 0112.03502