Abstract:
|
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. |