2006/03/18 by Chia-Fu Yu, Yu, Chia-Fu
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.math/0603451
Correct English errors, 15 pages
arxiv created 2007/06/23 · arxiv updated 2009/12/01
We give a unified formulation of a mass for arbitrary abelian varieties with PEL-structures and show that it equals a weighted class number of a reductive \Q-group G relative to an open compact subgroup U of G(\Af), or simply called an \it arithmetic mass. We classify the special objects for which our formulation remains valid over algebraic closed fields. As a result, we show that the set of basic points in a mod p moduli space of PEL-type with a local condition (and a mild condition subject to the Hasse principle) can be expressed as a double coset space and its mass equals an arithmetic mass. The moduli space does not need to have good reduction at p. This generalizes a well-known result for superspecial abelian varieties.