On the field of definition of superspecial polarized abelian varieties and type numbers

Tomoyoshi Ibukiyama; Toshiyuki Katsura

Compositio Mathematica (1994)

  • Volume: 91, Issue: 1, page 37-46
  • ISSN: 0010-437X

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Ibukiyama, Tomoyoshi, and Katsura, Toshiyuki. "On the field of definition of superspecial polarized abelian varieties and type numbers." Compositio Mathematica 91.1 (1994): 37-46. <http://eudml.org/doc/90280>.

@article{Ibukiyama1994,
author = {Ibukiyama, Tomoyoshi, Katsura, Toshiyuki},
journal = {Compositio Mathematica},
keywords = {abelian variety; positive characteristic; product of supersingular elliptic curves; Frobenius; principal polarization},
language = {eng},
number = {1},
pages = {37-46},
publisher = {Kluwer Academic Publishers},
title = {On the field of definition of superspecial polarized abelian varieties and type numbers},
url = {http://eudml.org/doc/90280},
volume = {91},
year = {1994},
}

TY - JOUR
AU - Ibukiyama, Tomoyoshi
AU - Katsura, Toshiyuki
TI - On the field of definition of superspecial polarized abelian varieties and type numbers
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 91
IS - 1
SP - 37
EP - 46
LA - eng
KW - abelian variety; positive characteristic; product of supersingular elliptic curves; Frobenius; principal polarization
UR - http://eudml.org/doc/90280
ER -

References

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  1. 1 Asai, T., The class number of positive definite quadratic forms, Japanese J. Math., 3 (1977) 239-296. Zbl0376.10017MR529280
  2. 2 Deuring, M., Die Anzahl der Typen von Maximalordnungen einer definiten Quatemionenalgebra mit primer Grundzahl, Jahresberich Deutschen Math., 54 (1951) 24-41. Zbl0039.02902MR36777
  3. 3 Deuring, M., Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Univ. Hamburg, 14 (1941) 197-272. Zbl0025.02003MR5125JFM67.0107.01
  4. 4 Eichler, M., Uber die Idealklassenzahl total definiter quaternionen algebren, Math. Z., 43 (1938) 102-109. Zbl0017.15003MR1545717JFM63.0093.02
  5. 5 Hartshorne, R., Algebraic Geometry, Springer, New York, Berlin, Heidelberg, 1977. Zbl0367.14001MR463157
  6. 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. Zbl0433.10017MR573338
  7. 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. Zbl0452.10029MR603952
  8. 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. Zbl0703.11019MR1040612
  9. 9 Ibukiyama, T., On rational points of curves of genus three over finite fields, to appear in Tohoku Math. J. Zbl0819.14007
  10. 10 Ibukiyama, T., Katsura, T. and Oort, F., Supersingular curves of genus two and class numbers, Compositio Math., 57 (1986) 127-152. Zbl0589.14028MR827350
  11. 11 Katsura, T. and Oort, F., Families of supersingular abelian surfaces, Compositio Math., 62 (1987) 107-167. Zbl0636.14017MR898731
  12. 12 Mumford, D., Abelian Varieties, Oxford University Press, 1970. Zbl0223.14022MR282985
  13. 13 Serre, J.-P., A letter to Hashimoto and Ibukiyama, 1984. 
  14. 14 Shimura, G., Arithmetic of alternating forms and quaternion hermitian forms, J. Math. Soc. Japan, 15 (1963) 33-65. Zbl0121.28102MR146172
  15. 15 Shimura, G. and Taniyama, Y., Complex Multiplication of Abelian Varieties and its Applications to Number Theory, Publ. Math. Soc. Japan6, 1961. Zbl0112.03502MR125113

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