All Questions

I am interested in understanding whether there are any significant connections between Calabi-Yau manifolds and number theory. Calabi-Yau manifolds are central objects in algebraic geometry and string ...

Elkies' supersingularity theorem: Given an elliptic curve $E$ over $\mathbb{Q}$, there are infinitely many primes $p$ such that $E$ is supersingular over $\mathbb{F}_p$. I have seen another post on ...

A weight 2 modular form which happens to be a normalised cuspidal eigenform with rational coefficients has a natural geometric avatar---namely an elliptic curve over the rationals. It seems to be a ...

The following is a theorem of Elkies: Let $X$ be an elliptic curve over $\mathbb{Q}$. Then there are infinitely many primes $p$ such that the action of Frobenius on $H^1(\mathcal{O}, X)$ is zero. ...