5 citations · 12 across the 22 of their papers we have counts for
9 papers · 1 filter
Profinite completions of products
Peter J. Haine
A source of difficulty in profinite homotopy theory is that the profinite completion functor does not preserve finite products. In this note, we provide a new, checkable criterion…
Exodromy beyond conicality
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
We show that compact subanalytic stratified spaces and algebraic stratifications of real varieties have finite exit-path -categories, refining classical theorems of Lefsche…
Descent for sheaves on compact Hausdorff spaces
Peter J. Haine
These notes explain some descent results for -categories of sheaves on compact Hausdorff spaces and derive some consequences. Specifically, given a compactly assembled $\in…
The fundamental fiber sequence in étale homotopy theory
Peter J. Haine, Tim Holzschuh, Sebastian Wolf
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…
Differential Cohomology: Categories, Characteristic Classes, and Connections
Araminta Amabel, Arun Debray, Peter J. Haine
We give an overview of differential cohomology from a modern, homotopy-theoretic perspective in terms of sheaves on manifolds. Although modern techniques are used, we base our disc…
The homotopy-invariance of constructible sheaves
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
The purpose of this paper is to explain why the functor that sends a stratified topological space to the -category of constructible (hyper)sheaves on with coefficie…
On the James and Hilton-Milnor Splittings, & the metastable EHP sequence
Sanath K. Devalapurkar, Peter J. Haine
This note provides modern proofs of some classical results in algebraic topology, such as the James Splitting, the Hilton-Milnor Splitting, and the metastable EHP sequence. We prov…
On the homotopy theory of stratified spaces
Peter J. Haine
Let be a poset. We define a new homotopy theory of suitably nice -stratified topological spaces with equivalences on strata and links inverted. We show that the exit-path co…
Exodromy
Clark Barwick, Saul Glasman, Peter Haine
Let be a quasicompact quasiseparated scheme. Write for the category whose objects are geometric points of and whose morphisms are specializations in…