Related papers: A descent spectral sequence for arbitrary K(n)-loc…

Let $E=E_n$ be Morava $E$-theory of height $n$. In previous work Devinatz and Hopkins introduced the $K(n)$-local $E_n$-Adams spectral sequence and showed that, under certain conditions, the $E_2$-term of this spectral sequence can be…

Let n \geq 1 and let p be any prime. Also, let E_n be the Lubin-Tate spectrum, G_n the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the…

We compute the continuous cohomology of the Morava stabilizer group with coefficients in Morava $E$-theory, $H^*(\mathbb{G}_2, E_t)$, at $p=2$, for $0\leq t < 12$, using the Algebraic Duality Spectral Sequence. Furthermore, in that same…

Using the pro\'etale site, we construct models for the continuous actions of the Morava stabiliser group on Morava E-theory, its $\infty$-category of $K(n)$-local modules, and its Picard spectrum. For the two sheaves of spectra, we evaluate…

Let $n \geq 1$, $p$ a prime, and $T(n)$ any representative of the Bousfield class of the telescope $v_n^{-1}F(n)$ of a finite type $n$ complex. Also, let $E_n$ be the Lubin-Tate spectrum, $K(E_n)$ its algebraic $K$-theory spectrum, and…

Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent spectral sequence for \pi_*(X^{hG})…

Let G be a closed subgroup of G_n, the extended Morava stabilizer group. Let E_n be the Lubin-Tate spectrum, let X be an arbitrary spectrum with trivial G-action, and define E^(X) to be L_K(n)(E_n ^ X). We prove that E^(X) is a continuous…

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…

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 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 prove that the Morava-$K$-theory-based Eilenberg-Moore spectral sequence has good convergence properties whenever the base space is a $p$-local finite Postnikov system with vanishing $(n+1)$st homotopy group.

We introduce a family of twisted $K(n)$-local theories that behave analogous to twisted K-theory. Let $R_n= E_n^{hS\mathbb G_n}$, the homotopy fixed point spectrum under the action of the subgroup $S\mathbb G_n$ of the Morava stabilizer…

When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not known, in general, how to form the iterated homotopy fixed point spectrum (Z^{hH})^{hK/H}, where Z is a continuous G-spectrum and all group actions…

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…

Let $p$ be a prime, $n \geq 1$, $K(n)$ the $n$th Morava $K$-theory spectrum, $\mathbb{G}_n$ the extended Morava stabilizer group, and $K(A)$ the algebraic $K$-theory spectrum of a commutative $S$-algebra $A$. For a type $n+1$ complex $V_n$,…

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…

In this note, we show how a continuous action of the Morava stabilizer group $\mathbb G_n$ on the Lubin-Tate spectrum $E_n$, satisfying the conclusion $E_n^{h\mathbb G_n}\simeq L_{K(n)} S$ of the Devinatz-Hopkins Theorem, may be obtained by…

We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope…

We calculate the homotopy type of $L_1L_{K(2)}S^0$ and $L_{K(1)}L_{K(2)}S^0$ at the prime 2, where $L_{K(n)}$ is localization with respect to Morava $K$-theory and $L_1$ localization with respect to $2$-local $K$ theory. In $L_1L_{K(2)}S^0$…

The Morava stabilizer groups play a dominating role in chromatic stable ho-motopy theory. In fact, for suitable spectra X, for example all finite spectra, thechromatic homotopy type of X at chromatic level n \textgreater{} 0 and a given…