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Results tagged with arithmetic-geometry
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user 53009
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
5
votes
1
answer
747
views
Elliptic curve and Galois representation
For an elliptic curve $E$ over ${\Bbb{Q}}$, let us consider Serre's mod $l$ representation by
$\rho_{E,l} \colon {\mathrm{Gal}}({\overline{\Bbb{Q}}}/{\Bbb{Q}}) \to {\mathrm{Aut}}(\phantom{}_lE) = {\ …
- 101
3
votes
2
answers
713
views
Elliptic curve E and Galois representation
Assume that an elliptic curve $E$ over $\Bbb Q$ has a reducible mod $p$ representation. Then
Q: Why is the semi-simplification of $E[p]$ the direct sum of ${\Bbb Z}/p{\Bbb Z}$ and $\mu_p$?
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Q …
- 101