J. Aust. Math. Soc.  78 (2005), 373-392

On the mass formula of supersingular abelian varieties with real multiplications

Chia-Fu Yu   Department of Mathematics   Columbia University   New York, NY 10027   USA   chiafu@math.columbia.edu

Abstract

A geometric mass concerning supersingular abelian varieties with real multiplications is formulated and related to an arithmetic mass. We determine the exact geometric mass formula for superspecial abelian varieties of Hilbert-Blumenthal type. As an application, we compute the number of the irreducible components of the supersingular locus of some Hilbert-Blumenthal varieties in terms of special values of the zeta function.

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