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

8 votes
2 answers
671 views

Is this lattice in the Tate module of an elliptic curve, coming from complex-analytic unifor...

Let $E$ be an elliptic curve over $\mathbb{Q}$, and let $p$ and $\ell$ be two distinct primes of good reduction. Let $T_\ell = T_\ell(E) = \varprojlim E[\ell^n](\overline{\mathbb{Q}})$ be the $\ell$-a …
Marc's user avatar
  • 374
4 votes
Accepted

Etale map has image whose complement is the vanishing locus of a finitely generated ideal

Let $U$ be the image of $\operatorname{Spec} B$ in $\operatorname{Spec} A$. Since the map $\operatorname{Spec} B \to \operatorname{Spec} A$ is open, $U$ is open. And since $\operatorname{Spec} B$ is q …
Marc's user avatar
  • 374
2 votes
0 answers
111 views

How to compute explicit equations for the Jacobian of a variety over a field [duplicate]

Suppose we start with a projective curve $X$ over a field $K$, given as a closed subvariety of $\mathbb P^n_K$ by some explicit list of equations. I would like to find an explicit representation of th …
Marc's user avatar
  • 374