* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory
* The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry
* Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry
Inhaltsverzeichnis
Beauville surfaces without real structures. - Couniformization of curves over number fields. - On the V-filtration of -modules. - Hecke orbits on Siegel modular varieties. - Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration. - Nested sets and Jeffrey-Kirwan residues. - Counting extensions of function fields with bounded discriminant and specified Galois group. - Classical and minimal models of the moduli space of curves of genus two. - Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve. - Mahler measure for dynamical systems on ? 1 and intersection theory on a singular arithmetic surface. - A Combination of the Conjectures of Mordell-Lang and André-Oort. - Motivic approach to limit sheaves. - Counting points on cubic surfaces, II. - Quantum cohomology of isotropic Grassmannians. - Endomorphism algebras of superelliptic jacobians.