The awe of formal geometry

An algebraic geometer sees an interesting nightmare in which all varieties become affine spaces. On the one hand, it makes life much easier. On the other hand, it means that there is not much to do in algebraic geometry. So this geometer wakes up in a cold sweat.

The goal of formal geometry is to bring this nightmare as close to the reality as possible. The origin of formal geometry is usuallyassociated with the names of Fuks, Gelfand and Kazhdan. In my talk I will follow mostly the exposition given in Sections 2 and 3 of http://arxiv.org/abs/1211.4230