Francois Loeser: On the homotopy type of Berkovich spaces
Abstract: To give some motivation, we shall start by reviewing some
work of Thuillier, Berkovich and Nicaise, showing that the topology of the
of an algebraic variety encodes important information about varieties and
their degenerations. We shall then present recent results obtained in
collaboration with Ehud Hrushovski:
Berkovich analytifications of algebraic varieties retract to finite
CW-complexes and are locally contractible. Our approach uses some advanced
tools from Model Theory.
We shall try to give at least some glimpses of what these are and what
are good for.