Related papers: Comodules and Landweber exact homology theories

This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of E(n)_*E(n)-comodules is equivalent to a…

In this paper we study quasi-categories of comodules over coalgebras in a stable homotopy theory. We show that the quasi-category of comodules over the coalgebra associated to a Landweber exact S-algebra depends only on the height of the…

In a previous paper, the authors showed that the category of E(n)_*E(n)-comodules is a localization of the category of BP_*BP-comodules. In this paper, we study the resulting localization functor L_n on the category of BP_*BP-comodules. It…

We define quasicategories of E_n-structured coalgebras, bialagebras and comodules. We show that: n-fold loop spaces, suspension spectra thereof, descent data for maps of E_n-ring spectra, descent corings of morphisms of E_n-ring spectra and…

We show that if $E$ is a $p$-local Landweber exact homology theory of height $n$ and $p > n^2+n+1$, then there exists an equivalence $h \mathcal{S}p_{E} \simeq h\mathcal{D}(E_{*}E)$ between homotopy categories of $E$-local spectra and…

We compute the mod(p) homotopy groups of the continuous homotopy fixed point spectrum E_2^{hH_2} for p>2, where E_n is the Landweber exact spectrum whose coefficient ring is the ring of functions on the Lubin-Tate moduli space of lifts of…

The bootstrap category in E-theory for C*-algebras over a finite space X is embedded into the homotopy category of certain diagrams of K-module spectra. Therefore it has infinite n-order for every n. The same holds for the bootstrap…

Building on work of Livernet and Richter, we prove that E_n-homology and E_n-cohomology of a commutative algebra with coefficients in a symmetric bimodule can be interpreted as functor homology and cohomology. Furthermore we show that the…

In this paper we study E^*BV_k, where E=BP<m,n> is a cohomology theory with coefficient ring F_p[v_m,...,v_n] (if m>0) or Z_(p)[v_1,...,v_n] (if m=0). We use ideas from the theory of multiple level structures, developed in earlier work of…

We investigate Hopf algebroids in the category of $L$-complete modules over a commutative Noetherian regular complete local ring. The main examples are provided by the Hopf algebroids associated to Lubin-Tate spectra in the K(n)-local…

We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as…

We show that the homotopy groups of a connective $E_k$-ring spectrum with an $E_k$-cell attached along a class $\alpha$ in degree $n$ are isomorphic to the homotopy groups of the cofiber of the self-map associated to $\alpha$ through degree…

We study the Picard group of Franke's category of quasi-periodic $E_0E$-comodules for $E$ a 2-periodic Landweber exact cohomology theory of height $n$ such as Morava $E$-theory, showing that for $2p-2 > n^2+n$, this group is infinite…

Let $\mathbb{k}$ be a commutative ring with global dimension zero. We show that we can rigidify homotopy coherent comodules in connective modules over the Eilenberg-Mac Lane spectrum of $\mathbb{k}$. That is, the $\infty$-category of…

Let $\mathbf{B}PU_{n}$ be the classifying space of $PU_n$, the projective unitary group of order $n$, for $n>1$. We use the Serre spectral sequence associated to a fiber sequence $\mathbf{B}U_n\rightarrow\mathbf{B}PU_n\rightarrow…

We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal…

We show that if $\Lambda$ is a $n$-Koszul algebra and $E=E(\Lambda)$ is its Yoneda algebra, then there is a full subcategory $\mathcal{L}_E$ of the category $Gr_E$ of graded $E$-modules, which contains all the graded $E$-modules presented…

If G is a finite group, some aspects of the modular representation theory depend on the cochains C^*(BG; k), viewed as a commutative ring spectrum. We consider its singularity category (in the sense of the author and Stevenson arxiv…

We introduce abelian framed bicategories, which are particular framed bicategories that are locally abelian, and show that they are suitable for developing homology and cohomology theories for directed structures. This means in particular…

It is classically known that Landweber exact homology theories (complex oriented theories which are completely determined by complex cobordism) admit no nontrivial phantom maps. Herein we propose a definition of $A$-Landweber exact spectra,…