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Results tagged with arithmetic-geometry
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user 5498
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
8
votes
Accepted
a question of Galois cohomology
The claimed triviality holds (the nonabelian cohomology set is not a group though), and I don't think you need $Char(K) \neq 2$. To argue this, I will use the long exact nonabelian cohomology sequence …
- 5,009
10
votes
Elliptic curve and Galois representation
None of these conditions implies that $E$ has good reduction at $p$. Consider, for instance, the elliptic curve $E = X_0(11)$, for which $E[5] \cong \mathbb{Z}/5\mathbb{Z} \oplus \mu_5$. Then for $l = …
- 5,009
6
votes
Elliptic curve E and Galois representation
Both questions have incorrect expectations. This has already been noted for the second question by S. Carnahan in the comments. For the first question, take any elliptic curve for which the semisimpli …
- 5,009
5
votes
Explicit calculation of Weil Deligne representations
Yes, it is possible. For all this explained clearly and in detail, see David Rohrlich's paper "Elliptic curves and the Weil-Deligne group" along with the accompanying "Student's supplement to "Ellipti …
- 5,009
16
votes
what is the maximum number of rational points of a curve of genus 2 over the rationals
I believe it is 642. See http://www.mathe2.uni-bayreuth.de/stoll/recordcurve.html
- 5,009