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math.AG2021★ 1 cited
Specialization for the pro-étale fundamental group
Piotr Achinger, Marcin Lara, Alex Youcis
For a formal scheme of finite type over a complete rank one valuation ring, we construct a specialization morphism \[ π^{\rm dJ}_1(\mathfrak{X}_η) \to π^{\rm proet}_…
math.AG2021
Geometric arcs and fundamental groups of rigid spaces
Piotr Achinger, Marcin Lara, Alex Youcis
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 o…
math.AG2021
A theorem on meromorphic descent and the specialization of the pro-étale fundamental group
Marcin Lara, Jiu-Kang Yu, Lei Zhang
Given a Noetherian formal scheme over , where is a complete DVR, we first prove a theorem of meromorphic descent along a possibly infinite cover of $\hat…