REVIEW 6 cited by
Pseudocoherent and Perfect Complexes and Vector Bundles on Analytic Adic Spaces
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
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.
Forward citations
Cited by 6 Pith papers
-
Cartier duality for gerbes of vector bundles
The Hodge-Tate stack of a smooth rigid variety is Cartier dual to the Simpson gerbe, so its solid quasi-coherent sheaves equal the weight-1 sheaves on the gerbe.
-
$p$-adic Fourier theory in families
The authors construct Fourier isomorphisms between function spaces on p-divisible rigid analytic groups and analytic functions on dual Z_p-local systems, over arbitrary small v-stacks, and apply them to build global E...
-
Representability of continuous K-theory in rigid analytic motivic $\mathbb{A}^1$-homotopy theory
Continuous K-theory of rigid analytic spaces is a Nisnevich sheaf, and, after A1-localization, it is represented by Z x BGL under a resolution-of-singularities assumption.
-
Topological Vector Spaces
A condensed version of the Topological Vector Spaces category is introduced, and fully faithful embeddings from algebraic p-adic vector spaces and from perfect complexes on the Fargues–Fontaine curve are proven.
-
An axiomatic approach to analytic $1$-affineness
An axiomatic framework proves 1-affineness for analytic Betti stacks, analytic de Rham stacks, and rigid analytic varieties, giving categorical Künneth formulas.
-
A motivic approach to rational $p$-adic cohomologies
Smooth complete intersections in projective toric varieties over p-adic fields satisfy the p-adic weight-monodromy conjecture, here re-proven through motivic nearby cycles and a monodromy-category equivalence.
Discussion (0). Continue with ORCID to comment.