Corpus ID: 235829131

Specialization for the pro-\'etale fundamental group

@inproceedings{Achinger2021SpecializationFT,
title={Specialization for the pro-\'etale fundamental group},
author={Piotr Achinger and Marcin Lara and Alex Youcis},
year={2021}
}
• Published 2021
• Mathematics
For a formal scheme X of finite type over a complete rank one valuation ring, we construct a specialization morphism
2 Citations

Figures from this paper

A theorem on meromorphic descent and the specialization of the pro-\'etale fundamental group
Given a Noetherian formal scheme X̂ over SpfpRq, where R is a complete DVR, we first prove a theorem of meromorphic descent along a possibly infinite cover of X̂. Using this we construct aExpand
Geometric arcs and fundamental groups of rigid spaces
• Mathematics
• 2021
We develop the notion of a geometric covering of a rigid space X, which yields a much larger class of covering spaces than that studied previously by de Jong. Geometric coverings of X are closedExpand

References

SHOWING 1-10 OF 38 REFERENCES
Étale Cohomology of Rigid Analytic Varieties and Adic Spaces
Summary of the results on the etale cohomology of rigid analytic varieties - Adic spaces - The etale site of a rigid analytic variety and an adic space - Comparison theorems - Base change theorems -Expand
Algebraic Number Theory
I: Algebraic Integers.- II: The Theory of Valuations.- III: Riemann-Roch Theory.- IV: Abstract Class Field Theory.- V: Local Class Field Theory.- VI: Global Class Field Theory.- VII: Zeta FunctionsExpand
The pro-\'etale topology for schemes
• Mathematics
• 2013
We give a new definition of the derived category of constructible $\ell$-adic sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamentalExpand
Extending families of curves over log regular schemes
Abstract In this paper, we generalize to the “log regular case” a result of de Jong and Oort which states that any morphism satisfying certain conditions from the complement of a divisor with normalExpand
Functorial desingularization of quasi-excellent schemes in characteristic zero: the nonembedded case
We prove that any reduced noetherian quasi-excellent scheme of characteristic zero admits a strong desingularization which is functorial with respect to all regular morphisms. As a main application,Expand
Vanishing cycles for formal schemes. II
Let k be a non-Archimedean field, and let X be a formal scheme locally finitely presented over the ring of integers k◦ (see §1). In this work we construct and study the vanishing cycles functor fromExpand
The pro-etale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes formerly known fundamental groups -- the usual etale fundamental group $\pi_1^{\mathrm{et}}$ defined in SGA1Expand