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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

0 votes
0 answers
96 views

Polynomial sparsity of conductors of elliptic curves

Let $f:\mathbb{N}\to\mathbb{N}$ be the map sending $n$ to the number of isomorphism classes of elliptic curves over $\mathbb{Q}$ with conductor $n$. Is there a polynomial $P$ such that $P(f(n))>n$ for …
Matias2's user avatar
  • 183
1 vote
0 answers
67 views

Curves covering elliptic curves with polynomially bounded genus

Let $S$ be the set of isomorphism classes of elliptic curves over $\mathbb{Q}$. Consider the following claim. There is a map $f:S\to \mathbb{N}$ such that $|f^{-1}(n)|$ is finite for all $n\in \mathb …
Matias2's user avatar
  • 183
15 votes
1 answer
336 views

Are there only finitely many $m$ such that $m$ is the number of elliptic curves with a given...

Let $f:\mathbb{N}\to\mathbb{N}$ be the map sending $n$ to the number of isomorphism classes of elliptic curves over $\mathbb{Q}$ with conductor $n$. Is $f(\mathbb{N})$ finite?
Matias2's user avatar
  • 183
2 votes
1 answer
157 views

Any finite number of curves over $\mathbb{Q}$ have a common cover

Given a finite number of algebraic curves over $\mathbb{Q}$ is there a curve that covers all of them?
Matias2's user avatar
  • 183