Topology of nonarchimedean analytic spaces |
Abstract: The usual norm on the complex numbers and its associated
analytic geometry (holomorphic functions and differential forms) have
been fundamental tools for understanding the geometry and topology of
complex algebraic varieties since the beginnings of the subject.
Nonarchimedean norms, such as the p-adic norm on the rational numbers,
also have an associated analytic geometry, which has been used
extensively in number theory, but is just beginning to be applied in
other areas of mathematics, such as algebraic geometry and dynamics.
Even the most basic topological properties of nonarchimedean analytic
spaces can be quite subtle. For instance, it was only in 2010 that
Hrushovski and Loeser proved that the nonarchimedean analytification
of an algebraic variety, in the sense of Berkovich, is locally
contractible and has the homotopy type of a finite simplicial complex. |
Web page: Alexandru I. Suciu | Comments to: andrei@neu.edu | |
Posted: November 21, 2012 | URL: http://www.math.neu.edu/bhmn/payne12.html |