# 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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