Ringed Spaces, Sheaves of Rings and Modules and Representation of a Ring as a Ring of Global Section

DMP-FCUP, sala 0.05
Thursday, 8 May, 2008 - 14:00

A ringed space is a pair (X, R) of a topological space X and a topological ring R, R is a sheaf of rings over the base space X. Rings are related to sheaves of rings in such a way that every ring can be represented as a ring of global sections of a ringed space (X, R) (by a global section we mean a continuous function from the topological space X to R). Our aim in this talk will be to define sheaves of rings, the decomposition space of a ring and then to give the basic topological properties of these notions. Then we show that every ring is isomorphic to a ring of global sections of a ringed space. At the end, we will give a characterization of biregular rings in terms of stalks of sheaves of rings to demonstrate the use of this representation, and how local results can be lifted to global results in special ringed spaces.

Speaker: 

Can Hatipoglu (Dokuz Eylul University and Universidade de Porto)