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Título:
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Abelian varieties with many endomorphisms and their absolutely simple factors
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Autor/a:
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Guitart Morales, Xavier
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
Abstract:
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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. |
Abstract:
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Peer Reviewed |
Materia(s):
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-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 |
Derechos:
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Tipo de documento:
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Artículo - Versión publicada Artículo |
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