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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
Accepted
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 …
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 …
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