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Results tagged with nt.number-theory
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user 78330
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
0
answers
275
views
Equations for Elliptic Curves
An elliptic curve $C$ over a field $k$ is a smooth, genus 1 curve defined over $k$ with an associated $k$-rational point. If char$(k) \ne 2$, we can show that $C$ has a model of the form $y^2 = f(x)$ …
- 109
3
votes
1
answer
399
views
Reduction of Abelian Varieties with Complex Multiplication have Complex Multiplication
Let $A$ be an abelian variety of dimension $g$ over $C$ with complex multiplication by a CM field $K$ where $[K:Q] =2g$. By this I mean that End($A$) $\cong \mathcal{O}_K$. Then, $A$ has a model over …
- 9,497