Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be m ...
The goal of the seminar is to learn the main aspects of class field theory, which aims at understanding abelian extensions of global fields in terms of the arithmetic of the field. The theory can also be seenas a first instance of the Langlands corresponde ...
Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using sche ...