On the mass formula of supersingular abelian varieties with real multiplications

• Autores: Chia-Fu Yu
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 78, Nº 3, 2005, págs. 373-392
• Idioma: inglés
• DOI: 10.1017/s1446788700008582
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• Resumen

  • 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.