Clay Summer School Arithmetic geometry, Göttingen 2006

Cover art, contributed by N. Elkies
Henri Darmon, David Ellwood, Brendan Hassett and Yuri Tschinkel, Editors' introduction, pdf
N. Elkies, On the cover: Rational curves on a K3 surface, pdf

H. Darmon, Rational points on curves, pdf
H. Chapdelaine, Non-abelian descent and the generalized Fermat equation, pdf
M. Rebolledo, Merel's theorem on the boundedness of the torsion of elliptic curves, pdf
P. Charollois, Generalized Fermat equations (d'après Halberstadt-Kraus), pdf
S. Dasgupta and J. Voight, Heegner points and Sylvester's conjecture, pdf
J. Voight, Shimura curve computations, pdf
M. Greenberg, Computing Heegner points arising from Shimura curve parametrizations, pdf
M. Greenberg, The arithmetic of elliptic curves over imaginary quadratic fields and Stark-Heegner points, pdf
Yu. I. Manin, Lectures on modular symbols, pdf

B. Hassett, Rational surfaces over nonclosed fields, pdf
D. Harari, Non-abelian descent, pdf
B. G. Vioreanu, Mordell-Weil Problem for Cubic Surfaces, Numerical Evidence, pdf

Y. Tschinkel, Algebraic varieties with many rational points, pdf
D. Abramovich, Birational geometry for number theorists, pdf
J. Starr, Arithmetic over function fields, pdf
N. Ratazzi, E. Ullmo, Galois+Equidistribution = Manin-Mumford, pdf
E. Ullmo, A. Yafaev, The Andre-Oort conjecture for products of modular curves, pdf
C.-L. Chai, F. Oort, Moduli of abelian varieties and p-divisible groups, pdf
D. Kaledin, Cartier isomorphism and Hodge Theory in the non-commutative case, pdf