We show that a large number of Thom spectra, i.e. colimits of morphisms BG → BGL1(S), can be obtained as iterated Thom spectra, i.e. colimits of morphisms BG → BGL1(M f ) for some Thom spectrum M f . This leads to a number of new relative Thom isomorphisms, e.g.As an example of interest to chromatic homotopy theorists, we also show that Ravenel's X(n) filtration of M U is a tower of intermediate Thom spectra determined by a natural filtration of BU by sub-bialagebras.
We define and study opfibrations of V-enriched categories when V is an extensive monoidal category whose unit is terminal and connected. This includes sets, simplicial sets, categories, or any locally cartesian closed category with disjoint coproducts and connected unit. We show that for an ordinary category B, there is an equivalence of 2categories between V-enriched opfibrations over the free V-category on B, and pseudofunctors from B to the 2-category of V-categories. This generalizes the classical (Set-enriched) Grothendieck correspondence.
We show that Boehmians defined over open sets of R N constitute a sheaf. In particular, it is shown that such Boehmians satisfy the gluing property of sheaves over topological spaces.MSC: Primary 44A40, 46F99; Secondary 44A35, 18F20
We show that Ravenel's spectrum X(2) is the versal E1-S-algebra of characteristic η. This implies that every E1-S-algebra R of characteristic η admits an E1-ring map X(2) → R, i.e. an A∞ complex orientation of degree 2. This implies that R * (CP 2 ) ∼ = R * [x]/x 3 . Additionally, if R is an E2-ring Thom spectrum admitting a map (of homotopy ring spectra) from X(2), e.g. X(n), its topological Hochschild homology has a simple description.
We define a notion of a connectivity structure on an ∞-category, analogous to a t-structure but applicable in unstable contexts-such as spaces, or algebras over an operad. This allows us to generalize notions of n-skeleta, minimal skeleta, and cellular approximation from the category of spaces. For modules over an Eilenberg-Mac Lane spectrum, these are closely related to the notion of projective amplitude.We apply these to ring spectra, where they can be detected via the cotangent complex and higher Hochschild homology with coefficients. We show that the spectra Y (n) of chromatic homotopy theory are minimal skeleta for HF 2 in the category of associative ring spectra. Similarly, Ravenel's spectra T (n) are shown to be minimal skeleta for BP in the same way, which proves that these admit canonical associative algebra structures.The authors would like to thank Jeremy Hahn for being a close part of questions and discussions that instigated this project, and Clark Barwick, Tim Campion, Ian Coley, and Denis Nardin for help with material related to this paper.This work is an outgrowth of conversations that took place while the authors were attending the workshop "Derived algebraic geometry and chromatic homotopy theory" during the Homotopy Harnessing Higher Structures program at the Isaac Newton Institute (EPSRC grant numbers EP/K032208/1 and EP/R014604/1).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.