Dr. Marcin Lara (Frankfurt):
On finite generation of fundamental groups in algebraic geometry
Time and place
Friday, 28.6.24, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Abstract
The étale fundamental group of a (quasicompact) variety over complex numbers is (topologically) finitely presented by comparison with the topological case.\nIn characteristic p, the situation is much more subtle, as affine varieties have very large fundamental groups.\nBuilding on a recent breakthrough result by Esnault, Shusterman and Srinivas, I will explain how to extend the finite presentation statement to arbitrary proper varieties (joint work with Srinivas and Stix) and then (at least the finite generation part) to log/tame fundamental groups of schemes and rigid analytic spaces (joint work with Achinger, Hübner and Stix).\nThis requires revisiting the tame topology of rigid spaces and working with a certain class of non-fs log schemes.