4 papers · 1 filter
Tame fundamental groups of rigid spaces
Piotr Achinger, Katharina Hübner, Marcin Lara +1
We introduce the tame étale fundamental group of a rigid space X over a non-archimedean field K. We show that if X is qcqs and K has topologically finitely generated t…
Logarithmic geometry beyond fs
Piotr Achinger, Katharina Hübner, Marcin Lara +1
We develop the foundations of logarithmic structures beyond the standard finiteness conditions. The motivation is the study of semistable models over general valuation rings. The k…
The étale topos reconstructs varieties over sub-p-adic fields
Magnus Carlson, Jakob Stix
Let be a sub--adic field. We show that the functor sending a finite type -scheme to its étale topos is fully faithful after localizing at the class of universal homeomorp…
Topological rigidity of maps in positive characteristic and anabelian geometry
Piotr Achinger, Jakob Stix
We study pairs of non-constant maps between two integral schemes of finite type over two (possibly different) fields of positive characteristic. When the target is quasi-affine, Ta…