Families of supersingular abelian surfaces

Toshiyuki Katsura; Frans Oort

Compositio Mathematica (1987)

  • Volume: 62, Issue: 2, page 107-167
  • ISSN: 0010-437X

How to cite

top

Katsura, Toshiyuki, and Oort, Frans. "Families of supersingular abelian surfaces." Compositio Mathematica 62.2 (1987): 107-167. <http://eudml.org/doc/89837>.

@article{Katsura1987,
author = {Katsura, Toshiyuki, Oort, Frans},
journal = {Compositio Mathematica},
keywords = {supersingular elliptic curve; standard divisor; Galois covering; principally polarized supersingular abelian surfaces; definite quaternion algebra; number of automorphisms of abelian surfaces},
language = {eng},
number = {2},
pages = {107-167},
publisher = {Martinus Nijhoff Publishers},
title = {Families of supersingular abelian surfaces},
url = {http://eudml.org/doc/89837},
volume = {62},
year = {1987},
}

TY - JOUR
AU - Katsura, Toshiyuki
AU - Oort, Frans
TI - Families of supersingular abelian surfaces
JO - Compositio Mathematica
PY - 1987
PB - Martinus Nijhoff Publishers
VL - 62
IS - 2
SP - 107
EP - 167
LA - eng
KW - supersingular elliptic curve; standard divisor; Galois covering; principally polarized supersingular abelian surfaces; definite quaternion algebra; number of automorphisms of abelian surfaces
UR - http://eudml.org/doc/89837
ER -

References

top
  1. 1 M. Deuring: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Sem. Univ. Hamburg14 (1941) 197-272. Zbl0025.02003MR5125JFM67.0107.01
  2. 2 M. Eichler: Über die Idealklassenzahl total definiter Quaternionenalgebren. Math. Z.43 (1938) 102-109. Zbl0017.15003MR1545717JFM63.0093.02
  3. 3 T. Ekedahl: On supersingular curves and abelian varieties. Prépublications Univ. de Paris-Sud, Orsay (1985). Zbl0641.14007
  4. 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. Zbl0493.10030MR603952
  5. 5 T. Ibukiyama, T. Katsura and F. Oort: Supersingular curves of genus two and class numbers. Comp. Math.57 (1986) 127-152. Zbl0589.14028MR827350
  6. 6 J. Igusa: Class number of a definite quaternion with prime discriminant. Proc. Nat. Acad. Sci. U.S.A.44 (1958) 312-314. Zbl0081.03601MR98728
  7. 7 J. Igusa: Arithmetic variety of moduli for genus two. Ann. of Math.72 (1960) 612-649. Zbl0122.39002MR114819
  8. 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. Zbl0656.14025MR946242
  9. 9 N. Koblitz: p-adic variation of the zeta-function over families defined over finite fields. Comp. Math.31 (1975) 119-218. Zbl0332.14008MR414557
  10. 10 L. Moret-Bailly: Polarizations de degré 4 sur les surfaces abéliennes. C.R. Acad. Sci. Paris289 (1979) 787-790. Zbl0432.14025MR558798
  11. 11 L. Moret-Bailly: Familles de courbes et de variétés abéliennes sur P1. Astérisque86 (1981) 109-140. Zbl0515.14006
  12. 12 D. Mumford: Abelian varieties. Oxford Univ. Press (1970). Zbl0223.14022MR282985
  13. 13 D. Mumford and J. Fogarty: Geometric invariant theory (second enlarged edition). Berlin-Heidelberg- New York: Springer-Verlag (1982). Zbl0504.14008MR719371
  14. 14 M.N. Narasimhan and M.V. Nori: Polarizations on an abelian variety. Geometry and analysis, Indian Acad. Sci. Bangalore (1980) 125-128. Zbl0509.14047
  15. 15 F. Oort: Subvarieties of moduli spaces. Invent. Math.24 (1974) 95-119. Zbl0259.14011MR424813
  16. 16 F. Oort: Which abelian surfaces are products of elliptic curves? Math. Ann.214 (1975) 35-47. Zbl0283.14007MR364264
  17. 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). Zbl0459.14008MR579026
  18. 18 G. Shimura: Arithmetic of alternating forms and quaternion hermitian forms. J. Math. Soc. Japan15 (1963) 33-65. Zbl0121.28102MR146172
  19. 19 T. Shioda: Supersingular K3 surfaces. Lecture Notes in Math.732, pp. 564-591. Berlin- Heidelberg-New York: Springer-Verlag (1979). Zbl0414.14019MR555718
  20. 20 W.C. Waterhouse: Abelian varieties over finite fields. Ann. Sci. Éc. Norm. Sup.4e série, t.2 (1969) 521-560. Zbl0188.53001MR265369
  21. 21 A. Weil: Zum Beweis des Torellischen Satzes. Nachr. Acad. Wiss. Göttingen Math. Phys. K1 (1957) 33-53. Zbl0079.37002MR89483

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.