Title: Zero-cycles over arithmetic fields.
Abstract: One of the motivating questions in Number Theory is finding integer solutions to diophantine equations. A famous example is the proof of Fermat's last theorem by Andrew Wiles. An equivalent question is to study the set of rational points on a smooth projective variety. Algebraic geometers on the other hand often study the classification of certain classes of varieties. In order to do so, they need to compute certain geometric or topological invariants, for example various cohomology groups.
In this talk, I will introduce such a geometric invariant that also relates to the study of points on varieties, namely the Chow group of zero-cycles on a smooth variety X. Experts have suggested several conjectures about the structure of this group over p-adic and algebraic number fields. By carrying out specific examples, I will explain the state of the art and will discuss some initial evidence towards the big conjectures. Part of this work is joint with Isabel Leal.