All Questions

For $K$ a number field, denote by $\mathcal{O}_K$ its ring of integers and by $H_K$ its Hilbert class field. For which imaginary quadratic field $K$ does there exist an elliptic curve $E$, defined ...

It's known that the class number of $\mathbb{Q}(\sqrt{p})$ is $1$ for all primes $p<229$. Question: What would it be like for conceptual explanations of $h(\mathbb{Q}(\sqrt{p}))=1$ for the first ...

Perhaps the most basic fact about abelian varieties with CM is they have an everywhere potential good reduction (Serre-Tate). On the face of it it might appear that there isn't much more to be added ...

If $f : X\to V$ is a smooth proper map of smooth schemes, what are the global sections of $R^if_{fppf, *}\mu_p$ $R^if_{fppf, *}\mathbb{G}_{\rm m}$ I was reading Milne's book "Arithmetic duality", ...

Question 0. Can a field of definitions (without automorphisms) of an (almost arbitrary) abelian variety of CM-type, originally defined over ${\mathbb{C}}$, be chosen to be a totally real number ...

I am currently learning some aspects of the theory of complex multiplication for elliptic curves, and the relationship with class field theory. As I understand it, there is a very special class of ...