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Results tagged with arithmetic-geometry
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user 6153
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
2
votes
When is the period of elliptic curve over the rationals transcendental?
You need to assume E defined over the algebraic numbers, or else "the" period makes no sense; and then there are two basic periods, except in the complex multiplication case where the ratio will be al …
- 12.6k
2
votes
Circles avoiding rational points of height $\le h$
A possible reformulation? If the equation of the circle is rational, then one rational point implies infinitely many. One sees that via lines of rational slope through the point, or the existence of a …
- 12.6k
3
votes
Good lecture notes/books on Jacobian of hyperelliptic curve
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 by Cassels and Flynn may help. That is, depending on whether the genus 2 case is enough to get started, and what type of questions you have …
- 12.6k
1
vote
Arithmetic geometry from a bird's-eye view
No, because there is the area called Diophantine geometry, and the formulation assumes it can be absorbed into "non-abelian class field theory" and "algebraic K-theory". We don't know that it can't, i …
- 12.6k
5
votes
Why certain diophantine equations are interesting (and others are not) ?
Picking up on the theme of the Hilbert problem on diophantine sets: we do know that they comprise all recursively enumerable sets. A diophantine set being only slightly more sophisticated than a given …
- 12.6k
3
votes
The historical development of automorphic geometry
Interesting take, but a bit hard to make into proper history, I should think.
Start with the idea that, post-Gauss, 19th century mathematics was mainly not about number theory. This could be hard to …
- 12.6k