Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudocoherent and Perfect Complexes and Vector Bundles on Analytic Adic
  Spaces   Using the new approach to analytic geometry developed by Clausen and Scholze
by means of condensed mathematics, we prove that for every affinoid analytic
adic space $X$, pseudocoherent complexes, perfect complexes, and finite
projective modules over $\mathcal{O}_X(X)$ form a stack with respect to the
analytic topology on $X$; in particular, we prove that the category of vector
bundles on $X$ is equivalent to the category of finite projective modules over
$\mathcal{O}_X(X)$. To that end, we construct a fully faithful functor from the
category of complete Huber pairs to the category of analytic rings in the sense
of Clausen and Scholze and study its basic properties. Specifically, we give an
explicit description of the functor of measures of the analytic ring associated
to a complete Huber pair. We also introduce, following the ideas of
Kedlaya-Liu, notions of \textit{pseudocoherent module} and
\textit{pseudocoherent sheaf} in the context of adic spaces (where the latter
can be regarded as an analogue of the notion of coherent sheaf in algebraic
geometry) and show that there is a similar equivalence of the corresponding
categories.

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The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess