Galois theory for (derived) commutative rings
Andrew Baker (University of Glasgow )
Wednesday 6th March 16:00-17:00 Maths 311B
Classical Galois theory of fields (as met in an undergraduate course) was generalised to commutative rings around 1960 by Auslander, Goldman, Chase, Harrison and Rosenburg. Around the same time, Grothendieck developed the theory of etale coverings of schemes and gave a more geometric view. In the ensuing half century the general framework has been expanded to many more settings including derived algebra. This talk will discuss the basic ideas that are common to these.
I will review the step from the field theory version to commutative rings, pointing out some of the extra tools required. If there is time I will explain some features of a derived version (originally developed in a topological context by Rognes).