Abelian varieties with many endomorphisms and their absolutely simple factors

作者：Guitart Xavier^*

来源：Revista Matematica Iberoamericana, 2012, 28(2): 591-601.

DOI：10.4171/RMI/686

• Abelian varieties of GL(2)-type
• k-varieties
• building blocks

We characterize the abelian varieties arising as absolutely simple factors of GL(2)-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 End(k)(0)(A) is a maximal subfield of End((k) over bar)(0)(A). We call them Ribet-Pyle varieties over k. We see that every Ribet-Pyle variety over k is isogenous over (k) over bar 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 GL(2)-type.

• 出版日期2012