Supersingular abelian varieties and modular forms

  • Tomoyoshi Ibukiyama | Osaka University

We give a survey on old and new results on relations between geometric invariants of principally polarized supersingular abelian varieties and arithmetic invariants of quaternion hermitian forms (such as the numbers of polarizations and irreducible components of the supersingular locus, the field of definition, existence of curves with many rational points, class numbers, type numbers, and Hecke operators).

Conjecturally quaternion hermitian forms are related with Siegel modular forms by Langlands philosophy.

So we also see where Siegel modular forms appear in the above theory.

Speaker Details

Born in 1948.Education: Undergraduate and Graduate course in the University of Tokyo under guidance of Professor Yasutaka Ihara.Employment: Assistant Prof. of Univ. Tokyo, Associate Prof. of Kyushu Univ., then Professor of Osaka Univ. until now.Mathematics: My Speciality is Number Theory, in particular Siegel modular forms, quadratic forms, various related zeta functions, and explicit calculation of all of them and their invariants.

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