Related papers: Picard groups of higher real $K$-theory spectra at…

We prove a colimit formula for the K-theory spectra of reductive p-adic groups of rank one with regular coefficients in terms of the K-theory of certain compact open subgroups. Furthermore, in the complex case, we show, using the…

Let $\operatorname{E}_2$ be the Morava E-theory of height 2 at the prime 2. In this paper, we compute the homotopy groups of $\operatorname{E}_2^{hC_6} \wedge \mathbb{R}P^2$ and $\operatorname{E}_2^{hC_6} \wedge \mathbb{R}P^2 \wedge…

Popov classified crystallographic complex reflection groups by determining lattices they stabilize. These analogs of affine Weyl groups have infinite order and are generated by reflections about affine hyperplanes; most arise as the…

We calculate the cohomology of the extended Morava stabilizer group of height $n$, with trivial mod $p$ coefficients, for all heights $n$ and all primes $p>>n$. The result is an exterior algebra on $n$ generators. A brief sketch of the…

Let $p$ be an odd prime and let $\mathit{EO} = E_{p-1}^{hC_p}$ be the $C_p$ fixed points of height $p-1$ Morava $E$ theory. We say that a spectrum $X$ has algebraic $\mathit{EO}$ theory if the splitting of $K_*(X)$ as an $K_*[C_p]$-module…

Let $H$ be a Hopf algebra, and $A$ an $H$-Galois extension. We investigate $H$-Morita autoequivalences of $A$, introduce the concept of $H$-Picard group, and we establish an exact sequence linking the $H$-Picard group of $A$ and the Picard…

For a profinite group $G$, we define an $S[[G]]$-module to be a certain type of $G$-spectrum $X$ built from an inverse system $\{X_i\}_i$ of $G$-spectra, with each $X_i$ naturally a $G/N_i$-spectrum, where $N_i$ is an open normal subgroup…

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum…

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 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 compute the first two k-invariants of the Picard spectra of $KU$ and $KO$ by analyzing their Picard groupoids and constructing their unit spectra as global sections of sheaves on the category of manifolds. This allows us to determine the…

We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with $\Z_2$-coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group,…

J McClure's Dyer-Lashof operation in $p$-adic $K$-theory defines, in particular, a prismatic structure on the complex representation ring of the circle group. Work of Ando, Rezk, Stapleton, and others generalizes this to define a canonical…

We introduce a computationally tractable way to describe the $\mathbb Z$-homotopy fixed points of a $C_{n}$-spectrum $E$, producing a genuine $C_{n}$ spectrum $E^{hn\mathbb Z}$ whose fixed and homotopy fixed points agree and are the…

We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving questions about convergence and differentials in the slice…

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…

We describe the Picard group of a tame stacky curve as an extension of two groups, which depend on the gerbe class of the curve over its rigidification, a stacky curve with trivial generic stabilizer, and the residual gerbes of the…

Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G…

The existence of a Picard-Vessiot extension for a homogeneous linear differential equation has been established when the differential field over which the equation is defined has an algebraically closed field of constants. In this paper, we…

We describe the slice tower and slice spectral sequence for arbitrary suspensions of the Eilenberg-MacLane spectrum of an arbitrary Mackey functor for the cyclic group of prime order.