Covers in -adic analytic geometry and log covers I: Cospecialization of the -tempered fundamental group for a family of curves
Emmanuel Lepage (2013)
Annales de l’institut Fourier
Similarity:
The tempered fundamental group of a -adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log...