p-Adic Analysis: A New Hope

Wojciech Wawrów (Oxford)

\(p\)-adic analysis is the theory of analytic functions over the field of \(p\)-adic numbers. Just like there are various differences between real and complex analysis, this theory is quite different from the familiar theory of analytic functions, these differences mainly stemming from the peculiar geometry of the field. One of the main difficulties in \(p\)-adic analysis is the lack of any sort of identity theorem, hence lack of a sensible notion of analytic continuation. In this talk we shall explore how Tate's rigid analytic geometry manages to circumvent these problems and lets one develop global geometry over non-Archimedean fields.