Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On fields of definition of components of the Siegel supersingular locus

Author: Chia-Fu Yu
Journal: Proc. Amer. Math. Soc. 145 (2017), 5053-5058
MSC (2010): Primary 11G15, 11G10
Published electronically: August 30, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Recently Ibukiyama proved an explicit formula for the number of certain non-principal polarizations on a superspecial abelian surface, extending his earlier work with Katsura for principal polarizations [Compos. Math. 91 (1994), 37-46]. As a consequence of Ibukiyama's formula, there exists a geometrically irreducible component of the Siegel supersingular locus which is defined over the prime finite field. In this note we give a direct proof of this result.

References [Enhancements On Off] (What's this?)

  • [1] T. Ibukiyama, Quinary lattices and binary quaternion hermitian lattices, preprint, 2016. To appear in Tohoku Math. J.
  • [2] T. Ibukiyama, Type numbers of quaternion hermitian forms and supersingular abelian varieties, preprint, 2016. To appear in Osaka J. Math.
  • [3] Tomoyoshi Ibukiyama and Toshiyuki Katsura, On the field of definition of superspecial polarized abelian varieties and type numbers, Compositio Math. 91 (1994), no. 1, 37–46. MR 1273924
  • [4] Toshiyuki Katsura and Frans Oort, Families of supersingular abelian surfaces, Compositio Math. 62 (1987), no. 2, 107–167. MR 898731
  • [5] Ke-Zheng Li and Frans Oort, Moduli of supersingular abelian varieties, Lecture Notes in Mathematics, vol. 1680, Springer-Verlag, Berlin, 1998. MR 1611305
  • [6] Chia-Fu Yu, The supersingular loci and mass formulas on Siegel modular varieties, Doc. Math. 11 (2006), 449–468. MR 2288077
  • [7] C.-F. Yu, On arithmetic of the superspecial locus, arXiv:1210.1120v2. To appear in Indiana Univ. Math. J.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11G15, 11G10

Retrieve articles in all journals with MSC (2010): 11G15, 11G10

Additional Information

Chia-Fu Yu
Affiliation: Institute of Mathematics, Academia Sinica, 6th Floor, Astronomy Mathematics Building, No. 1, Roosevelt Road Section 4, Taipei, Taiwan, 10617 – and – National Center for Theoretical Sciences, No. 1 Roosevelt Road Section 4, National Taiwan University, Taipei, Taiwan, 10617

Keywords: Superspecial abelian surfaces, supersingular locus, field of definition
Received by editor(s): December 5, 2016
Published electronically: August 30, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society