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Results tagged with nt.number-theory
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user 15630
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
11
votes
0
answers
1k
views
Linear algebra of elliptic curves over p-adic fields
Unfortunately, the following question is somewhat ill-posed. However, I hope to make what I'm looking for sufficiently clear.
Given two elliptic curves (or Abelian varieties) over $\mathbb{C}$, one c …
- 1,537
8
votes
l-adic Turrittin
Here's a naive formulation of an analogue, which is false. (This fits very well the conditional phrasing from your question, since it would be an analogue if it were true!)
Levelt-Turrittin says that …
- 1,537
4
votes
2
answers
544
views
Maps preserving algebraic numbers
Suppose $f:\mathbb{C}\to\mathbb{C}$ is a map with your favorite smoothness condition (say, $C^1, C^{\infty}$ or holomorphic) and suppose that $f(\overline{\mathbb{Q}})\subset\overline{\mathbb{Q}}$. Is …
- 1,537
21
votes
What's the "best" proof of quadratic reciprocity?
There was some discussion above about how the proof with Gauss sums is hard to motivate. I disagree, but the motivation involves a little more (mild) algebraic number theory (i.e., Galois theory, alge …
- 1,537