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.

**Knowl status:**

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

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**History:**(expand/hide all)

- 2020-10-12 09:30:05 by Edgar Costa (Reviewed)
- 2020-09-26 15:09:06 by John Voight
- 2020-09-26 15:04:59 by John Voight
- 2018-05-24 17:11:43 by John Cremona (Reviewed)

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