Related papers: Homological localizations of Eilenberg-Mac Lane sp…

We prove definable versions of the Universal Coefficient Theorems of Eilenberg--Mac Lane expressing the (Steenrod) homology groups of a compact metrizable space in terms of its integral cohomology groups, and the (\v{C}ech) cohomology…

A. K. Bousfield's $H\mathbb Z$-localization of groups inverts homologically two-connected homomorphisms of groups. J. P. Levine's algebraic closure of groups inverts homomorphisms between finitely generated and finitely presented groups…

We study the logarithmic topological Hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory. Our results apply, for example, to connective covers of periodic ring spectra like…

In this article we study localisation of spectral sums $\{S_R\}_{R > 0}$ associated to the sub-Laplacian $\mathcal{L}$ on the Heisenberg Group $\mathbb{H}^d$ where $S_R f := \int_0^R dE_{\lambda }f$, with $\mathcal{L} = \int_0^{\infty}…

The paper is devoted to study the space of multiplicative maps from the Eilenberg-MacLane spectrum $H\Z$ to an arbitrary ring spectrum $R$. We try to generalize the approach of Schwede from "Formal groups and stable homotopy of commutative…

Let $G$ be a finite group. For a based $G$-space $X$ and a Mackey functor $M$, a topological Mackey functor $X\widetilde\otimes M$ is constructed, which will be called the stable equivariant abelianization of $X$ with coefficients in $M$.…

We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of these groups, in the category of $E_\infty$-algebras, guided…

We give a simple algebraic model for rational G-spectra over an exceptional subgroup, for any compact Lie group G. Moreover, all our Quillen equivalences are symmetric monoidal, so as a corollary we obtain a monoidal algebraic model for…

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…

We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a…

Let G be an algebraic group and let X be a smooth integral scheme over a field k. In this paper we construct homology-type groups $H_i(X,G)$ by considering cycles in the simplicial scheme $BG\times X (an idea suggested by Andrei Suslin). We…

We describe the formal properties of cellularization functors in triangulated categories and study the preservation of ring and module structures under these functors in stable homotopy categories in the sense of Hovey, Palmieri and…

Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $\mathcal{D}(R)$ denote the derived category of $R$-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let $X$ be a…

Hopkins and Mahowald gave a simple description of the mod $p$ Eilenberg Mac Lane spectrum $\mathbb{F}_p$ as the free $\mathbb{E}_2$-algebra with an equivalence of $p$ and $0$. We show for each faithful $2$-dimensional representation…

We compute the slices and slice spectral sequence of integral suspensions of the equivariant Eilenberg-Mac Lane spectra $H\underline{\mathbb{Z}}$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors…

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional $gl_2$-modules. As a byproduct we show that there…

We offer a complete description of $THH(E(2))$ under the assumption that the Johnson-Wilson spectrum $E(2)$ at a chosen odd prime carries an $E_\infty$-structure. We also place $THH(E(2))$ in a cofiber sequence $E(2) \rightarrow…

Let $R$ be a ring spectrum and $ E\to X$ an $R$-module bundle of rank $n$. Our main result is to identify the homotopy type of the group-like monoid of homotopy automorphisms of this bundle, $hAut^R(E)$. This will generalize the result…

Colocalization is a right adjoint to the inclusion of a subcategory. Given a ring-spectrum R, one would like a spectral sequence which connects a given colocalization in the derived category of R-modules and an appropriate colocalization in…

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of…