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Results tagged with arithmetic-geometry
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user 56286
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
7
votes
0
answers
190
views
Almost rational point
Let $X$ be a variety over a number field $K$. Let $S$ be a finite set of places of $K$. Is there a notion of a point $p \in X(\overline{K})$ to be "almost rational" in the following sense?:
$p$ and $ …
- 463
3
votes
1
answer
487
views
Trivial Weil-Châtelet group
Does there exist an elliptic curve over a number field $K$ such that $WC(E/K)\cong H^1(G_K, E)$ is trivial?
- 463
26
votes
4
answers
1k
views
Variety acquiring rational point over any quadratic extension
Does there exist a variety $X$ over $\mathbb{Q}$ (or a number field) such that it has no rational points over $\mathbb{Q}$ but acquires points over any quadratic extension $\mathbb{Q}(\sqrt{d})$?
If …
- 463