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Results tagged with arithmetic-geometry
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user 51424
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
35
votes
Accepted
IMO 2017/6 via arithmetic geometry
The set $S$ gives rise to a subscheme (which let's also denote by $S$) of $\mathbb{P}^1_{\mathbb{Z}},$ because relatively a prime pair $(x,y)$ corresponds to a section of $\mathbb{P}^1_{\mathbb{Z}}\ri …
- 5,958
10
votes
Accepted
Points on affine hypersurface over finite field
Note that the defining equation for $X$ can be rewritten as
$$(x+y)^3+(x-y)^3+(z+w)^3+(z-w)^3=-2.$$
As the linear transformation $(x,y,z,w)\mapsto(x+y,x-y,z+w,z-w)$ is invertible over any field of cha …
- 5,958