Let $ X $ be a quasicompact quasiseparated scheme. Write $\operatorname {Gal}(X) $ for
the category whose objects are geometric points of $ X $ and whose morphisms are …

Many important theorems in differential topology relate properties of manifolds to properties
of their underlying homotopy types--defined eg using the total singular complex or the\v {C} …

Many important theorems in differential topology relate properties of manifolds to properties
of their underlying homotopy types–defined eg using the total singular complex or the Čech …

Let be a field with separable closure, and let be a qcqs-scheme. We use the theory of
profinite Galois categories developed by Barwick–Glasman–Haine to provide a quick …

For a log scheme locally of finite type over ℂ, a natural candidate for its profinite homotopy
type is the profinite completion of its Kato–Nakayama space. Alternatively, one may consider …

This paper has two main goals. First, we prove nonabelian refinements of basechange
theorems in étale cohomology (ie, prove analogues of the classical statements for sheaves …

The main goal of this paper is to set a foundation for homotopy theory of algebraic stacks
under model category theory and to show how it can be applied in various contexts. It not …

We complete the program, initiated in [6], to compare the many different possible definitions
of the underlying homotopy type of a log scheme. We show that, up to profinite completion …

We study a symplectic variant of algebraic K-theory of the integers, which comes equipped
with a canonical action of the absolute Galois group of Q. We compute this action explicitly …

The goal of this paper is to establish an equivalence of profinite completions of pro-spaces
in model category theory and in∞-category theory. As an application, we show that the …