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Results tagged with elliptic-curves
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user 2039
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.
5
votes
When does the module of Katz modular forms contain a basis for the vector space of classical...
I do not think that your definition of Katz modular form is exactly correct. A (Katz) weight-$k$ modular form for $\Gamma$ is a section of the line bundle on $\mathcal{Y}(\Gamma)_R$ that evaluates on …
- 12.1k
2
votes
Accepted
Non-vanishing modular forms
I will answer Q2:
N=2: Denote by $Y^1(2)$ the moduli of elliptic curves with point of order 2 and fixed invariant differential. It is not hard to show that $Y^1(2) = \mathrm{Spec}\, \mathbb{Z}[\frac12 …
- 12.1k
4
votes
A reference for $\mathbb{A}^1_R$ being a coarse moduli space of the stack of elliptic curves
The following strategy should work although I do not claim that it is the most elegant.
Claim 1: The coarse moduli stack of elliptic curves $\mathcal{M}_{1,R}$ is affine.
Proof: It is enough to sho …
- 12.1k
5
votes
Accepted
Reference for universal elliptic curves
For any $n\geq 1$, one can define a functor $\mathcal{M}_1(n)\colon \mathrm{Schemes}/\mathbb{Z}[\frac1n] \to \mathrm{Groupoids}$, sending a scheme to the groupoid of elliptic curves over it with a cho …
- 12.1k
1
vote
0
answers
109
views
Compactifications of product of universal elliptic curves
Let $\mathcal{E}$ be the universal elliptic curve over the moduli stack $\mathcal{M}$ of elliptic curves. As $\mathcal{E}$ is an abelian group scheme over $\mathcal{M}$, we obtain a product-preserving …
- 12.1k