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Why H Z-algebra Spectra are Differential Graded Algebras?
Related publications (146)
Quasi-categories vs. Segal spaces: Cartesian edition
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: 1.On marked simplicial sets (due to Lurie [31]), 2.On bisimplicial spaces (due to deBrito [12]), 3.On bisimplicial sets, 4.On m ...
2021The cotangent complex and Thom spectra
The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of E-infinity-ring spectra in various ways. In this work we first establish, in the context o ...
2021Conjugation spaces are cohomologically pure
Conjugation spaces are equipped with an involution such that the fixed points have the same mod 2 cohomology (as a graded vector space, a ring, and even an unstable algebra) but with all degrees divided by 2, generalizing the classical examples of complex ...
WILEY2021On the stress tensor light-ray operator algebra
Grégoire Olivier Mathys, Matthew Thomas Walters, Alexandre Mathieu Frédéric Belin
We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...
2021The algebra of Boolean matrices, correspondence functors, and simplicity
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
2020A Distributed Cyber-Attack Detection Scheme With Application to DC Microgrids
Giancarlo Ferrari Trecate, Mustafa Sahin Turan
DC microgrids often present a hierarchical control architecture, requiring integration of communication layers. This leads to the possibility of malicious attackers disrupting the overall system. Motivated by this application, in this article, we present a ...
2020The uniform symbolic topology property for diagonally F-regular algebras
Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...
2020Towards the K(2)-local homotopy groups of Z
Previously (Adv. Math. 360 (2020) art. id. 106895), we introduced a class (Z) over tilde of 2-local finite spectra and showed that all spectra Z is an element of (Z) over tilde admit a v(2)-self-map of periodicity 1. The aim here is to compute the K(2)-loc ...
GEOMETRY & TOPOLOGY PUBLICATIONS2020Applications of one-point extensions to compute the A∞-(co)module structure of several Ext (resp., Tor) groups
Let A be a nonnegatively graded connected algebra over a noncommutative separable k-algebra K, and let M be a bounded below graded right A-module. If we denote by T the -coalgebra , we know that there exists an -comodule structure on over T. The structure ...
2019Simple and projective correspondence functors
A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. We determine exactly which simple correspondence functors are projective. We also determine which simple ...
2019