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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
4
votes
Is every $GL_2(\mathbb{Z}/n\mathbb{Z})$-extension contained in some elliptic curve's torsion...
Two comments. First, there is a trick used by Serre, Ribet and others to prove, using an old result of Goursat, that under certain assumptions such as absolute irreducibility, two mod p Galois represe …