Oberseminar Wintersemester 2020/21

Speaker: Marco Maculan (Jussieu)

Date, time & place: November 12, 2020, 4:45 pm, via Zoom

Title: Affine vs. Stein in complex and p-adic geometry

Abstract: A complex manifold is said to be Stein if it can be holomorphically embedded in an affine space. Of course, complex affine varieties are Stein. However the converse fails to be true: Serre exhibited a non-affine algebraic group (the universal vector extension of an elliptic curve) biholomorphic to an affine group (the product of two copies of the multiplicative group). In a joint project with J. Poineau, we investigate the p-adic (or more generally non-Archimedean) analog of this phenomenon. Despite the formal similarities between complex and p-adic analytic theories, to our surprise the p-adic picture is much more rigid. In the talk I will recall the complex situation and then focus on the main ideas/examples making the p-adic results so different.