Results 31 to 40 of about 3,488 (119)

Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions [PDF]

, 2019
Let $X$ be a Noetherian separated and finite dimensional scheme over a field $\mathbb{K}$ of characteristic zero. The goal of this paper is to study deformations of $X$ over a differential graded local Artin $\mathbb{K}$-algebra by using local Tate ...
Manetti, Marco, Meazzini, Francesco
core   +3 more sources

Enriched Reedy categories [PDF]

, 2015
We define the notion of an enriched Reedy category, and show that if A is a C-Reedy category for some symmetric monoidal model category C and M is a C-model category, the category of C-functors and C-natural transformations from A to M is again a model ...
Angeltveit, Vigleik
core   +2 more sources

(Co-)fibration of generalized crossed modules

AIMS Mathematics
Crossed modules are algebraic structures that generalize the concept of group extensions. They involve group-like objects (often groups or groupoids) with additional structure and mappings between them that satisfy certain properties. Generalized crossed
Hatice Gülsün Akay
doaj   +1 more source

On Fico's Lemmata and the homotopy type of certain gyrations

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We undertake to determine the homotopy type of gyrations of sphere products and of connected sums, thereby generalising results known in earlier literature as ‘Fico's Lemmata’ which underpin gyrations in their original formulation from geometric topology.
Sebastian Chenery
wiley   +1 more source

Modeling (∞,1)$(\infty,1)$‐categories with Segal spaces

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract In this paper, we construct a model structure for (∞,1)$(\infty,1)$‐categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of (∞,1)$(\infty,1)$‐categories given by complete Segal spaces and Segal categories.
Lyne Moser, Joost Nuiten
wiley   +1 more source

Model category structures on truncated multicomplexes for complex geometry

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4163-4177, December 2025.
Abstract To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to N$N$‐multicomplexes. We present a family of model category structures on the category of N$N$‐multicomplexes where the weak equivalences are the morphisms inducing a quasi‐isomorphism ...
Joana Cirici, Muriel Livernet, Sarah Whitehouse   +2 more
wiley   +1 more source

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source

The localization sequence for the algebraic K-theory of topological K-theory

, 2006
We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage
Andrew J. Blumberg, C. Ausoni, C. Ausoni, J. E. McClure, Michael A. Mandell   +4 more
core   +2 more sources

Parametrized stability and the universal property of global spectra

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop a framework of parametrized semiadditivity and stability with respect to so‐called atomic orbital subcategories of an indexing ∞$\infty$‐category T$T$, extending work of Nardin. Specializing this framework, we introduce global ∞$\infty$‐categories and the notions of equivariant semiadditivity and stability, yielding a higher ...
Bastiaan Cnossen, Tobias Lenz, Sil Linskens   +2 more
wiley   +1 more source

Purity, ascent and periodicity for Gorenstein flat cotorsion modules

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract We investigate purity within the Frobenius category of Gorenstein flat cotorsion modules, which can be seen as an infinitely generated analogue of the Frobenius category of Gorenstein projective objects. As such, the associated stable category can be viewed as an alternative approach to a big singularity category, which is equivalent to Krause'
Isaac Bird
wiley   +1 more source