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In this paper, we introduce a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. We discuss various properties of quasi-projective dimension. Among other things, we prove the…

Commutative Algebra · Mathematics 2021-08-18 Mohsen Gheibi , David A. Jorgensen , Ryo Takahashi

We introduce a notion of Milnor square of stable $\infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision…

Algebraic Geometry · Mathematics 2024-09-24 Tom Bachmann , Adeel A. Khan , Charanya Ravi , Vladimir Sosnilo

We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…

Functional Analysis · Mathematics 2023-12-15 Andreas Debrouwere , Jasson Vindas

We study the structure of families of well approximable elements of tensor products of Banach spaces including analogs of the classical quasianalytic classes in the sense of Bernstein and Beurling. As in the case of quasianalytic functions,…

Classical Analysis and ODEs · Mathematics 2015-05-14 Alexander Brudnyi

In the first part of the paper, we formulate several arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in the presence of ramification. The ramification comes from the choice of…

Number Theory · Mathematics 2026-05-05 Chao Li , Michael Rapoport , Wei Zhang

We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of…

Operator Algebras · Mathematics 2013-06-19 José Carrión , Marius Dadarlat , Caleb Eckhardt

We make explicit some conditions on a semi-abelian category D such that, for any abelian group A in D and any object Y in D, the cohomology group homomorphisms with coefficients in A, induced by the inclusion of the abelian objects of D at…

Category Theory · Mathematics 2010-01-12 Dominique Bourn

It is proved that the category of simplicial complete bornological spaces over $\mathbb R$ carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is…

Differential Geometry · Mathematics 2017-07-31 Dennis Borisov , Kobi Kremnizer

In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…

Category Theory · Mathematics 2018-01-29 Osman Mucuk , Serap Demir

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…

Algebraic Topology · Mathematics 2016-02-03 Moritz Groth , Jan Šťovíček

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

Representation Theory · Mathematics 2014-05-06 Robert Boltje , Susanne Danz

This paper brings together C*-algebras and algebraic topology in terms of viewing a C*-algebraic invariant in terms of a topological spectrum. E-theory, E(A,B), is a bivariant functor in the sense that is a cohomology functor in the first…

Operator Algebras · Mathematics 2017-08-11 Sarah L. Browne

For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent sheaves. In another application, we show…

Algebraic Geometry · Mathematics 2012-06-04 Yu-Han Liu , Hsian-Hua Tseng

Given a Frobenius category $\mathcal{F}$ satisfying certain finiteness conditions, we consider the localization of its Hall algebra $\mathcal{H(F)}$ at the classes of all projective-injective objects. We call it the {\it "semi-derived Hall…

Quantum Algebra · Mathematics 2014-09-25 Mikhail Gorsky

We give a moduli-theoretic proof of the classical theorem of Gabriel, stating that a scheme can be reconstructed from the abelian category of quasi-coherent sheaves over it. The methods employed are elementary and allow us to extend the…

Algebraic Geometry · Mathematics 2013-10-25 John Calabrese , Michael Groechenig

In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to study semibricks from the point of view of $\tau$-tilting…

Representation Theory · Mathematics 2018-06-07 Sota Asai

We introduce a relative tilting theory in abelian categories and show that this work offers a unified framework of different previous notions of tilting, ranging from Auslander-Solberg relative tilting modules on Artin algebras to…

Representation Theory · Mathematics 2023-11-27 Alejandro Argudin Monroy , Octavio Mendoza Hernandez

We prove that the category of Stein spaces and holomorphic maps is anti-equivalent to the category of Stein algebras and $\mathbb{C}$-algebra morphisms. This removes a finite dimensionality hypothesis from a theorem of Forster.

Complex Variables · Mathematics 2026-03-03 Olivier Benoist

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting…

Category Theory · Mathematics 2015-03-03 Emily Riehl , Dominic Verity

In this paper we define a family of theories, quasi-theories, motivated by quasi-elliptic cohomology. They can be defined from constant loop spaces. With them, the constructions on certain theories can be made in a neat way, such as those…

Algebraic Topology · Mathematics 2018-09-19 Zhen Huan