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

8 votes
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Are all anabelian Galois actions faithful?

The answer is "yes" I think, even if you replace $\mathbb Q$ with a number field. In the affine case this is a result of Matsumoto, as pointed out by Felipe Voloch, see Matsumoto, Makoto Galois rep …
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2 votes
Accepted

Ideal class groups and extension of number fields

if your aim is really to relate $Pic(Y)$ to $Pic (X)$ it is probably a good idea to pybass the use of $\mathcal Q$ and to consider instead the more powerful technique of introducing the relative Picar …
Niels's user avatar
  • 4,008
5 votes

Proofs of Mordell-Weil theorem

I think one should also mention Jean Pierre Serre Lectures on the Mordell-Weil Theorem Aspects of Mathematics
Niels's user avatar
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