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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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 …
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