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Related papers: Theorems A and B for dagger quasi-Stein spaces

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Using $L^2$-methods, we prove a vanishing theorem for tame harmonic bundles over quasi-compact K\"ahler manifolds in a very general setting. As a special case, we give a completely new proof of the Kodaira type vanishing theorems for Higgs…

Algebraic Geometry · Mathematics 2022-04-26 Ya Deng , Feng Hao

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated…

Algebraic Geometry · Mathematics 2023-06-22 Jorge António , Mauro Porta

We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the…

Category Theory · Mathematics 2020-12-11 Aran Tattar

We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and…

Category Theory · Mathematics 2025-11-18 Matthew Di Meglio , Chris Heunen

Let $A$ and $B$ be $C^*$-algebras with $A\subseteq M(B)$. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in $A$ and $B$, we identify conditions that allow to…

Operator Algebras · Mathematics 2020-11-03 B. K. Kwaśniewski , R. Meyer

The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this…

Category Theory · Mathematics 2012-09-24 Jamie Vicary

We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic…

Algebraic Geometry · Mathematics 2025-12-15 Xuanyou Li , Chenhan Liu

We define quasi--locally presentable categories as big unions of coreflective subcategories which are locally presentable. Under appropriate hypotheses we prove a representability theorem for exact contravariant functors defined on a…

Category Theory · Mathematics 2012-05-11 George Ciprian Modoi

In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's…

General Topology · Mathematics 2019-03-18 Yaé Ulrich Gaba

We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in \cite{DL23} for the extremal black hole horizons and completes the…

Differential Geometry · Mathematics 2026-05-12 Alex Colling , Maciej Dunajski

We introduce a category of 'rigid spaces with overconvergent structure sheaf' which we call dagger spaces --- this is the correct category in which de Rham cohomology in rigid analysis should be studied. We compare it with the (usual)…

Algebraic Geometry · Mathematics 2014-08-15 Elmar Grosse-Klönne

In this paper, we define vector bundles within the framework of almost mathematics (referred to as almost vector bundles) and establish the $v$-descent theorem together with a structure theorem for these bundles over perfectoid spaces. The…

Algebraic Geometry · Mathematics 2026-01-28 Yuntong Cui , Guo Li , Shuhan Jiang , Jiahong Yu

In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi-BPS categories (called BPS in this case) are…

Algebraic Geometry · Mathematics 2024-09-18 Tudor Pădurariu , Yukinobu Toda

This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the analogy with the development of homological algebra for abelian…

Algebraic Geometry · Mathematics 2017-03-14 Alain Connes , Caterina Consani

We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ring $R^*$ from the DG-category of DG-modules over a DG-ring…

Category Theory · Mathematics 2025-10-08 Leonid Positselski

We introduce pseudocubical objects with pseudoconnections in an arbitrary category, obtained from the Brown-Higgins structure of a cubical object with connections by suitably relaxing their identities, and construct a cubical analog of the…

K-Theory and Homology · Mathematics 2009-07-14 Irakli Patchkoria

We prove that the K-theory of an exact quasicategory can be computed via a higher categorical variant of the Q construction. This construction yields a quasicategory whose weak homotopy type is a delooping of the K-theory space. We show…

K-Theory and Homology · Mathematics 2013-07-05 C. Barwick

In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…

Rings and Algebras · Mathematics 2023-10-06 Shoutao Guo , Li Liang

We introduce the categories of quasi-measurable spaces, which are slight generalizations of the category of quasi-Borel spaces, where we now allow for general sample spaces and less restrictive random variables, spaces and maps. We show…

Probability · Mathematics 2021-09-27 Patrick Forré

We prove a desingularization theorem for the quasi-smooth derived scheme, in the sense of Hekking. We also propose the conjecture that the K-theoretic integration of the virtual fundamental class of a quasi-smooth derived scheme could be…

Algebraic Geometry · Mathematics 2023-06-21 Yu Zhao