Mathematics Colloquium — Special Lecture
Spring 2012
Anthony Várilly-Alvarado
Rice University
Explicit Arithmetic on Algebraic Surfaces
The geometric complexity of a variety is a good proxy for its arithmetic complexity. Using the classification of algebraic surfaces as a guide for geometric complexity, we will discuss explicit techniques for computing cohomological obstructions to the existence and distribution of rational points on algebraic surfaces, with a view toward identifying a boundary between arithmetically “well-behaved” varieties, like rational surfaces, and arithmetically “wild” varieties, like surfaces of general type.