Seminar: Non-archimedean geometry

Marcin Lara

Abstract: We introduce a new category of covering spaces in rigid geometry, called geometric coverings, and show it is classified by a certain topological fundamental group. Geometric coverings generalize the class of étale coverings, introduced by de Jong, and its various natural modifications, and have certain desirable properties that were missing from those older notions: they are étale local and closed under taking infinite disjoint unions. The definition is based on the property of unique lifting of “geometric arcs.” On the way, we answer some questions from the foundational paper of de Jong. This is joint work with Piotr Achinger and Alex Youcis.