5 citations · 12 across the 22 of their papers we have counts for
25 papers
The derived moduli of perverse sheaves
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
We construct higher derived Artin stacks parametrizing constructible sheaves on complex algebraic varieties and compact real analytic varieties. Furthermore, we show that every per…
Classifying anima of condensed -categories of points
Peter J. Haine
We compare the classifying anima of two natural condensed -categories associated to a coherent -topos. One from our work with Barwick and Glasman on exit-path categ…
Localizing invariants of constructible sheaves
Qingyuan Bai, Peter J. Haine
Given an open-closed decomposition of the stratifying poset, we construct a new semi-orthogonal decomposition of the -category of constructible sheaves on a stratified spac…
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…
Standard -structures
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
We provide a general construction of induced -structures, that generalizes standard -structures for -categories of sheaves. More precisely, given a presentable $\inft…
Fully faithful functors and pushouts of -categories
Peter J. Haine, Maxime Ramzi, Jan Steinebrunner
We study stability properties of fully faithful functors, and compute mapping anima in pushouts of -categories along fully faithful functors. We provide applications of the…
Reconstruction of schemes from their étale topoi
Magnus Carlson, Peter J. Haine, Sebastian Wolf
Let be a field that is finitely generated over its prime field. In Grothendieck's anabelian letter to Faltings, he conjectured that sending a -scheme to its étale topos defi…
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…
Spectral weight filtrations
Peter J. Haine, Piotr Pstrągowski
We provide a description of Voevodsky's -category of motivic spectra in terms of the subcategory of motives of smooth proper varieties. As applications, we construct weight…
Nonabelian basechange theorems & étale homotopy theory
Peter J. Haine, Tim Holzschuh, Sebastian Wolf
This paper has two main goals. First, we prove nonabelian refinements of basechange theorems in étale cohomology (i.e., prove analogues of the classical statements for sheaves of s…
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…
From nonabelian basechange to basechange with coefficients
Peter J. Haine
The goal of this paper is to explain when basechange theorems for sheaves of spaces imply basechange for sheaves with coefficients in other presentable -categories. We acco…
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…
Pyknotic objects, I. Basic notions
Clark Barwick, Peter Haine
Pyknotic objects are (hyper)sheaves on the site of compacta. These provide a convenient way to do algebra and homotopy theory with additional topological information present. This…
On coherent topoi & coherent -localic -topoi
Peter J. Haine
In this note we prove the following useful fact that seems to be missing from the literature: the -category of coherent ordinary topoi (in the sense of SGA4) is equivalent…
Exodromy for stacks
Clark Barwick, Peter Haine
In this short note we extend the Exodromy Theorem of arXiv:1807.03281 to a large class of stacks and higher stacks. We accomplish this by extending the Galois category construction…
Extended étale homotopy groups from profinite Galois categories
Peter J. Haine
In this note we show that the protruncated shape of a spectral -topos is a delocalization of its profinite stratified shape. This gives a way to reconstruct the extended ét…
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…
Lifting Enhanced Factorization Systems to Functor -Categories
Peter J. Haine
In this paper we give sufficient conditions for lifting an enhanced factorization system on a -category to the functor -cate…