Related papers: Comparison of Morava E-theories

We study the relationship between the transchromatic localizations of Morava $E$-theory, $L_{K(n-1)}E_n$, and formal groups. In particular, we show that the coefficient ring $\pi_0L_{K(n-1)}E_n$ has a modular interpretation, representing…

We investigate a dense subgroup Gamma of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Gamma acts on the Bruhat-Tits building for GL_2(Q_l)…

The Bousfield-Kan (or unstable Adams) spectral sequence can be constructed for various homology theories such as Brown-Peterson homology theory BP, Johnson-Wilson theory $E(n)$, or Morava $E$-theory $E_n$. For nice spaces the $E_2$-term is…

The Morava $E$-theories, $E_{n}$, are complex-oriented $2$-periodic ring spectra, with homotopy groups $\mathbb{W}_{\mathbb{F}_{p^{n}}}[[u_{1}, u_{2}, ... , u_{n-1}]][u,u^{-1}]$. Here $\mathbb{W}$ denotes the Witt vector ring. $E_{n}$ is a…

We describe a vanishing result on the cohomology of a cochain complex associated to the moduli of chains of finite subgroup schemes on elliptic curves. These results have applications to algebraic topology, in particular to the study of…

The fixed point spectra of Morava E-theory $E_n$ under the action of finite subgroups of the Morava stabilizer group $\mathbb{G}_n$ and their K(n)-local Spanier--Whitehead duals can be used to approximate the K(n)-local sphere in certain…

Let A be an A_\infty ring spectrum. We use the description from [2] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another…

The problem addressed is the classification up to conjugation of the finite subgroups of the (classical) Morava stabilizer group S_n and the extended Morava stabilizer group G_n(u) associated to a formal group law F of height n over the…

We consider $G=Q_8,SD_{16},G_{24},$ and $G_{48}$ as finite subgroups of the Morava stabilizer group which acts on the height $2$ Morava $E$-theory $\mathbf{E}_2$ at the prime $2$. We completely compute the $G$-homotopy fixed point spectral…

Let $E_n$ be Morava $E$-theory and let $G \subset G_n$ be a finite subgroup of $G_n$, the extended Morava stabilizer group. Let $E_{n}^{tG}$ be the Tate spectrum, defined as the cofiber of the norm map $N:(E_n)_{hG} \to E_n^{hG}$. We use…

This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their…

At large primes, the height $n$ Ravenel-May spectral sequence takes as input the cohomology of a certain solvable Lie $\mathbb{F}_p$-algebra, and produces as output the mod $p$ cohomology of the height $n$ strict Morava stabilizer group…

We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing…

We introduce the Morava-isotropic stable homotopy category and, more generally, the stable homotopy category of an extension $E/k$. These "local" versions of the Morel-Voevodsky stable ${\Bbb{A}}^1$-homotopy category $SH(k)$ are analogues…

We prove the convergence of the Adams spectral sequence based on Morava K-theory and relate it to the filtration by powers of the maximal ideal in the Lubin-Tate ring through a Miller square. We use the filtration by powers to construct a…

We compute the algebraic Morava K-theory ring of split special orthogonal and spin groups. In particular, we establish certain stabilization results for the Morava K-theory of special orthogonal and spin groups. Besides, we apply these…

We deform the Ravenel-Wilson computation of the Morava K-homology of Eilenberg-Mac Lane spaces to obtain a similar description of their completed Morava E-homology. This yields both a cohomological description and an interpretation on the…

We compute recursive approximations of the action of the height $h \geq 2$ Morava stabilizer group on the associated Lubin-Tate deformation ring. We then specialize to the case $h=3$ and $p>2$ to calculate the action explicitly. These…

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…

By the work of Brodzki-Niblo-Nowak-Wright and Monod, topological amenability of a continuous group action can be characterized using uniformly finite homology groups or bounded cohomology groups associated to this action. We show that…