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Francesco Polizzi
Francesco Polizzi
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Dimensions Dimension of the moduli space of abelian varieties with a prescribed endomorphism algebra

Let $D$ be a division algebra over a number field $K$, and consider abelian varieties $A$ over the complex numbers, of dimension $g$ with an action of (an order of) $D$. Is it known when this set is non-empty, and if so what is the dimension of this space?

I always thought this was a solved question but glancing over the literature it seems like it might be tricky. Is there a good reference?

Thanks!

Dimensions of moduli of abelian varieties with a prescribed endomorphism algebra

Let $D$ be a division algebra over a number field $K$, and consider abelian varieties $A$ over the complex numbers, of dimension $g$ with an action of (an order of) $D$. Is it known when this set is non-empty, and if so what is the dimension of this space?

I always thought this was a solved question but glancing over the literature it seems like it might be tricky. Is there a good reference?

Thanks!

Dimension of the moduli space of abelian varieties with a prescribed endomorphism algebra

Let $D$ be a division algebra over a number field $K$, and consider abelian varieties $A$ over the complex numbers, of dimension $g$ with an action of (an order of) $D$. Is it known when this set is non-empty, and if so what is the dimension of this space?

I always thought this was a solved question but glancing over the literature it seems like it might be tricky. Is there a good reference?

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jacob
jacob
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Dimensions of moduli of abelian varieties with a prescribed endomorphism algebra

Let $D$ be a division algebra over a number field $K$, and consider abelian varieties $A$ over the complex numbers, of dimension $g$ with an action of (an order of) $D$. Is it known when this set is non-empty, and if so what is the dimension of this space?

I always thought this was a solved question but glancing over the literature it seems like it might be tricky. Is there a good reference?

Thanks!