Work

Topological Vector Spaces

Year: 2025

Type: preprint

Abstract: Motivated by applications to duality theorems for $p$-adic pro-étale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full subcategories, both the category of (topologically) bounded algebraic Vector Spaces and the category of perfect complexes on the Fargues-Fontaine curve. Vector Spaces coming from $p$-adic pro-étale cohomology of smooth partially proper rigid analytic varieties are examples of sheaves belonging to the former category.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2509.25981

Authors: Colmez, Pierre, Nizioł, Wiesława

Institution: Sorbonne Université

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Hausdorff Research Institute for Mathematics

Awards: G3010527862, Cohomology of locally symmetric spaces

OpenAlex ID: W4414975384

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