| Títol: | Abelian varieties with many endomorphisms and their absolutely simple factors |
| Autor: | Guitart Morales, Xavier |
| Altres autors/autores: | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
| Matèries: | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Abelian varieties
Arithmetical algebraic geometry.
Varietats abelianes
Esquemes (Geometria algebraica)
Geometria algebraica aritmètica
Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry)
Classificació AMS::14 Algebraic geometry::14K Abelian varieties and schemes |
| Tipus de document: | Article |
| Descripció: | We characterize the abelian varieties arising as absolutely simple
factors of GL2-type varieties over a number field k. In order to obtain
this result, we study a wider class of abelian varieties: the k-varieties A/k
satisfying that End0
k(A) is a maximal subfield of End0
¯k
(A). We call them
Ribet–Pyle varieties over k. We see that every Ribet–Pyle variety over k
is isogenous over ¯k to a power of an abelian k-variety and, conversely,
that every abelian k-variety occurs as the absolutely simple factor of some
Ribet–Pyle variety over k. We deduce from this correspondence a precise
description of the absolutely simple factors of the varieties over k of
GL2-type. |
| Altres identificadors i accés: | Guitart, X. Abelian varieties with many endomorphisms and their absolutely simple factors. "Revista matemática iberoamericana", 2012, vol. 28, núm. 2, p. 591-601.
0213-2230
http://hdl.handle.net/2117/16194
10.4171/rmi/686 |
| Disponible al dipòsit: | E-prints UPC
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