Specialization for the pro-etale fundamental group

Date: 2021-11-17

Time: 13:30 - 14:30

Zoom link: https://kva-se.zoom.us/j/9217561880


Piotr Achinger


We provide a natural extension of Grothendieck’s theory of specialization for the etale fundamental group in the context of rigid-analytic geometry. More precisely, for a formal scheme of finite type over a complete dvr, we define a specialization map from the de Jong fundamental group of the rigid-analytic generic fiber to the pro-etale fundamental group of the special fiber. We apply similar ideas to study the notion of tameness for etale coverings of non-archimedean spaces, which requires the use of logarithmic geometry in the form of the logarithmic Abhyankar’s lemma.

This is joint work with Marcin Lara and Alex Youcis.