2 citations · 6 across the 9 of their papers we have counts for
9 papers
The condensed homotopy type of a scheme
Peter J. Haine, Tim Holzschuh, Marcin Lara +3
We study a condensed version of the étale homotopy type of a scheme, which refines both the usual étale homotopy type of Friedlander-Artin-Mazur and the proétale fundamental group…
Fundamental groups of proper varieties are finitely presented
Marcin Lara, Vasudevan Srinivas, Jakob Stix
It was recently proven by Esnault, Shusterman and the second named author, that the étale fundamental group of a connected smooth projective variety over an algebraically closed fi…
Variants of the de Jong fundamental group
Piotr Achinger, Marcin Lara, Alex Youcis
For a rigid space , we answer two questions of de Jong about the category of coverings which are locally in the admissible topology on the disj…
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}_…
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…
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…
Homotopy Exact Sequence for the Pro-Étale Fundamental Group II
Marcin Lara
The pro-étale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes the usual étale fundamental group defined in SGA1 and leads to an inte…
On the inverse problem for deformations of finite group representations
Marcin Lara
Let be even and . We show that the ring is a quotient of the universal deformation ring of a representation of a finite group. This…
Fundamental Exact Sequence for the Pro-Étale Fundamental Group
Marcin Lara
The pro-étale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes formerly known fundamental groups -- the usual étale fundamental group …