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19 votes
3 answers
2k views

Elkies' supersingularity theorem in higher dimension

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. ...
David E Speyer's user avatar
12 votes
0 answers
729 views

Elkies' supersingularity theorem in higher dimension (in terms of the associated Newton polygon)

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 ...
Catherine Ray's user avatar
1 vote
0 answers
264 views

Are there connections between Calabi-Yau manifolds and number theory?

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 ...
Abdullah M Al-jazy's user avatar