Localisation in algebra and geometry

Jorge Vitoria, University of Stuttgart

Lecture series 

Ring-theoretical localisation is a set of techniques used to invert
elements in a ring. In these lectures we will study these techniques,
starting with commutative rings and with their geometric counterparts,
and we will aim to develop some geometric intuition for localisation
ideas in noncommutative algebra. An essential tool for this will be
the use of torsion-theoretical ideas in the category of modules, to
which a geometric flavour is, therefore, assigned.