Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the \'etale homotopy type of higher stacks   A new approach to \'etale homotopy theory is presented which applies to a
much broader class of objects than previously existing approaches, namely it
applies not only to all schemes (without any local Noetherian hypothesis), but
also to arbitrary higher stacks on the \'etale site of such schemes, and in
particular to all algebraic stacks. This approach also produces a more refined
invariant, namely a pro-object in the infinity category of spaces, rather than
in the homotopy category. We prove a profinite comparison theorem at this level
of generality, which states that if $\mathcal{X}$ is an arbitrary higher stack
on the \'etale site of affine schemes of finite type over $\mathbb{C},$ then
the \'etale homotopy type of $\mathcal{X}$ agrees with the homotopy type of the
underlying stack $\mathcal{X}_{top}$ on the topological site, after profinite
completion. In particular, if $\mathcal{X}$ is an Artin stack locally of finite
type over $\mathbb{C}$, our definition of the \'etale homotopy type of
$\mathcal{X}$ agrees up to profinite completion with the homotopy type of the
underlying topological stack $\mathcal{X}_{top}$ of $\mathcal{X}$ in the sense
of Noohi. In order to prove our comparison theorem, we provide a modern
reformulation of the theory of local systems and their cohomology using the
language of $\infty$-categories which we believe to be of independent interest.

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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics