Simple mass formulas on Shimura varieties of PEL-type
| dc.creator | Yu, Chia-Fu | |
| dc.date | 2006-03-18 | |
| dc.date | 2007-06-23 | |
| dc.date.accessioned | 2026-07-07T08:11:59Z | |
| dc.date.available | 2026-07-07T08:11:59Z | |
| dc.description | 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 $G(\A_f)$, 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. | |
| dc.description | Correct English errors, 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603451 | |
| dc.identifier | http://arxiv.org/abs/math/0603451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132303 | |
| dc.subject | Number Theory | |
| dc.title | Simple mass formulas on Shimura varieties of PEL-type | |
| dc.type | text |