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Results tagged with elliptic-curves
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user 4008
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
2
votes
Fields obtained by adjoining x coordinates of torsion points on elliptic curves
I think this works: Take two non-isogenous (over $\overline{K}$) curves $E$ and $E'$ with $K(E[\ell])=K(E'[\ell])=K$. Replace $E'$, say, by a quadratic twist. Then $K(E[\ell])=K(x(E[\ell]))=K(x(E'[\el …
- 22.6k
9
votes
Square of an elliptic curve and projective plane
What we have here is a special case of the following (well-known) construction:
Starting with a smooth and proper curve $C$ we may consider its symmetric power
$S^nC=C^n/\Sigma_n$. It (because we are …
- 22.6k
18
votes
About isogeny theorem for elliptic curves
If all Tate modules (i.e., for all $\ell$) are isomorphic then they differ by
the twist by a locally free rank $1$ module over the endomorphism ring of one of
them. This is true for all abelian variet …
- 22.6k
8
votes
Accepted
Is there a presentation of the cohomology of the moduli stack of torsion sheaves on an ellip...
It seems that one can obtain the additive structure of rational cohomology
without too much effort (in no way have I checked this carefully so caveat
lector applies). As Allen noticed, for rational co …
- 22.6k