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Results tagged with arithmetic-geometry
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user 25341
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
1
vote
1
answer
215
views
Is the number of twists of a curve with a section in a given field finite
Let $X$ be a smooth projective geometrically connected curve over a number field $k$ of genus $g\geq 2$.
Is the number of twists of $X$ always infinite? (The answer is no, because there aren't any tw …
- 281
27
votes
6
answers
4k
views
Does the moduli space of smooth curves of genus g contain an elliptic curve
Let $M_g$ be the moduli space of smooth projective geometrically connected curves over a field $k$ with $g\geq 2$. Note that $M_g$ is not complete.
Does $M_g$ contain an elliptic curve?
The answer i …
- 281