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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
Minimal polynomial of symmetric endomorphism on abelian variety
Yes. The $\mathbb{Q}$-algebra $B$ generated by $f$ is a finite-dimensional $\mathbb{Q}$-algebra with a positive involution, hence semisimple. It is also commutative, hence a product of fields. The min …
1
vote
isogeny and congruence subgroup
The image in $\text{PSL}_2(\mathbb{Q})$ of a congruence subgroup of $\text{SL}_2(\mathbb{Q})$ need not be a congruence subgroup (hence doesn't contain one).
Incidentally, for any reductive group $G$ …