Geometria em Lisboa lecture series and minicourses showcase introductions to topics of interest in Geometry.

A Gentle Introduction to Grothendieck's Theory of Schemes
A mini course by Herwig  Hauser, University of Vienna

At the end of the 1950s, Alexandre Grothendieck coined the concept of "Schemes" as a natural generalization of the classical notion of algebraic variety. Based on the conviction that geometry should be understood axiomatically in terms of the underlying algebraic structures — ideals, rings and homomorphisms between them — the introduction of schemes led to a (pacific) revolution in modern algebraic geometry, producing a language and machinery which was and still is able to prove numerous known theorems and many new ones in a much more natural and deeper fashion.

The course will provide a systematic description of the bottlenecks one encounters in trying to design such a theory, and how, miraculously, all these obstacles can be resolved thus making Grothendieck's program work so fabulously.

No special knowledge is needed, a basic formation in algebra will, however, be helpful (quotient rings, finitely generated algebras, prime and maximal ideals, prime factorization, local rings, tensor product,...).

The course will be understandable for Master's students and also ambitious Bachelor's students.

All sessions in the Department of Mathematics, Room P3.10.