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On the mass formula of supersingular abelian varieties with real multiplications

Part of: Discontinuous groups and automorphic forms Forms and linear algebraic groups

Published online by Cambridge University Press:  09 April 2009

Chia-Fu Yu
Chia-Fu Yu
Affiliation:
Department of MathematicsColumbia UniversityNew York, NY 10027USA e-mail: chiafu@math.columbia.edu
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Abstract

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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 Hubert-Blumenthal type. As an application, we compute the number of the irreducible components of the supersingular locus of some Hubert-Blumenthal varieties in terms of special values of the zeta function.

Keywords

mass formulasupersingular locussuperspecial abelian varietiesHilbert-Blumenthal varieties

MSC classification

Secondary: 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11E41: Class numbers of quadratic and Hermitian forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 3 , June 2005 , pp. 373 - 392
Copyright
Copyright © Australian Mathematical Society 2005

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