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A simple abelian variety $A$ is said to be of $\textbf{GL}_2$-type if its endomorphism algebra $\mathrm{End}(A)\otimes\Q$ is commutative and has dimension (as a $\Q$-vector space) equal to the dimension of $A$ (as an abelian variety). More generally, an abelian variety is said to be of $\textbf{GL}_2$-type if it is isogenous (over the ground field) to a product of pairwise non-isogenous simple abelian varieties of $\textrm{GL}_2$-type.

A curve is said to be of $\text{GL}_2$-type if its Jacobian is of $\text{GL}_2$-type.

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• Review status: reviewed
• Last edited by Edgar Costa on 2020-10-12 09:30:05
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