Arithmetic Geometry

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About the cover: Rational curves on a K3 surface
Curves: Rational points on curves
Non-abelian descent and the generalized Fermat equation
Merel's theorem on the boundedness of the torsion of elliptic curves
Generalized Fermat equations (d'apres Halberstadt-Kraus)
Heegner points and Sylvester's conjecture
Shimura curve computations
Computing Heegner points arising from Shimura curve parametrizations
The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points
Lectures on modular symbols
Surfaces: Rational surfaces over nonclosed fields
Non-abelian descent
Mordell-Weil problem for cubic surfaces, numerical evidence
Higher-dimensional varieties: Algebraic varieties with many rational points
Birational geometry for number theorists
Arithmetic over function fields
Galois + Equidistribution = Manin-Mumford
The Andre-Oort conjecture for products of modular curves
Moduli of abelian varieties and $p$-divisible groups
Cartier isomorphism and Hodge theory in the non-commutative case
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