Corestriction of central simple algebras and families of Mumford-type
- Volume: 10, Issue: 3, page 191-211
- ISSN: 1120-6330
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topGalluzzi, Federica. "Corestriction of central simple algebras and families of Mumford-type." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.3 (1999): 191-211. <http://eudml.org/doc/252418>.
@article{Galluzzi1999,
abstract = {Let \( M \) be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra \( A \) over a real cubic number field and imposing a condition to the corestriction of such \( A \). In this paper, under some extra conditions on the algebra \( A \), we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple \( CM \)-fibers and we give a method to construct a family of Mumford-type starting from such a fiber.},
author = {Galluzzi, Federica},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Abelian varieties; CM-type; Corestriction; Hodge group; family of Mumford-type; abelian fourfolds; Mumford-Tate group; Hodge structure},
language = {eng},
month = {9},
number = {3},
pages = {191-211},
publisher = {Accademia Nazionale dei Lincei},
title = {Corestriction of central simple algebras and families of Mumford-type},
url = {http://eudml.org/doc/252418},
volume = {10},
year = {1999},
}
TY - JOUR
AU - Galluzzi, Federica
TI - Corestriction of central simple algebras and families of Mumford-type
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/9//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 3
SP - 191
EP - 211
AB - Let \( M \) be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra \( A \) over a real cubic number field and imposing a condition to the corestriction of such \( A \). In this paper, under some extra conditions on the algebra \( A \), we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple \( CM \)-fibers and we give a method to construct a family of Mumford-type starting from such a fiber.
LA - eng
KW - Abelian varieties; CM-type; Corestriction; Hodge group; family of Mumford-type; abelian fourfolds; Mumford-Tate group; Hodge structure
UR - http://eudml.org/doc/252418
ER -
References
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