Chennai Mathematical Institute


CMI Mathematics Seminar
Date: Tuesday, May 18, 2021.
Time: 2:00 PM.
Fundamental groups in non-archimedean geometry

Piotr Achinger
Institute of Mathematics of Polish Academy of Science, (IMPAN), Warsaw, Poland.


One of the main reasons non-archimedean geometry is useful to an algebraic geometer is the appearance of covering spaces of infinite degree. Key examples include Tate's uniformization of elliptic curves, its generalizations due to Mumford and Raynaud, and the theory of p-adic period mappings. At the same time, a comprehensive theory of the fundamental group of rigid spaces remains elusive. A major step in this direction has been taken by de Jong, who studied morphisms which locally on the base (in the sense of Berkovich analytic geometry) are disjoint unions of finite etale coverings. I will describe a vast generalization of this, based on the idea that good 'covering spaces' can be characterized by the property of 'unique arc lifting'. This is joint work with Marcin Lara and Alex Youcis.