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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

0 votes
1 answer
50 views

Rational functions on elliptic curves over global fields with given support

Let $E$ be an elliptic curve over a global field $k$. Let $x_1, \dots, x_r$ be a set of generators of $E(k) / E(k)_{tor}$ (or more generally, a $\mathbb Q$-basis of $E(k)_{\mathbb Q}$), and let $x_0$ …
yoyo's user avatar
  • 67
4 votes
1 answer
150 views

About the reduction type of the Kodaira symbol of elliptic curves defined over p-adic local ...

Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $E$ be an elliptic curve defined over $K$. Tate's algorithm can be used to compute the Kodaira symbol of the reduction type of $E$. However, I …
yoyo's user avatar
  • 67
2 votes
1 answer
65 views

Questions about elliptic curves with level-$n$ structure

Let $n$ be a positive integer, which is $4$ or a prime number $l$. Let $E$ be an elliptic curve defined over a number field $K$. Assume that all the $n$-torsion points of $E$ are defined over $K$, i.e …
yoyo's user avatar
  • 67