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Results tagged with arithmetic-geometry
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user 8441
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
15
votes
Are there any rational solutions to this equation?
As Dror says, according to Sage it's a genus 2 curve. Homogenizing your equation gives a degree 4 projective plane curve $C$, with arithmetic genus thus $(d-1)(d-2)/2 = 3\cdot 2/2 = 3$. The geometri …
- 2,368
17
votes
Accepted
Roadmap to Computer Algebra Systems Usage for Algebraic Geometry
Your question is "Which computer algebra system is best for what, and what is the easiest/most fun(?) way to learn how to deal with them?"
Regarding community, I think Sage (http://sagemath.org) …
17
votes
Accepted
Upper bounds for ranks of modular jacobians
The rank of J0(389) over Q is 13.
The Jacobian splits into factors of dimensions 1,2,3,6,20. Combining explicit computation with Kolyvagin-Gross-zagier implies that the factors of dim 20 has rank 0. …
- 2,368