Related papers: An introduction to algebraic models for rational G…

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds…

In this paper, we introduce the notion of $G_\infty$-ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their equivariant homotopy and cohomology groups. We…

We show that one can use model categories to construct rational orthogonal calculus. That is, given a continuous functor from vector spaces to based spaces one can construct a tower of approximations to this functor depending only on the…

Let G be a finite group. We give Quillen equivalent models for the category of G-spectra as categories of spectrally enriched functors from explicitly described domain categories to nonequivariant spectra. Our preferred model is based on…

Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spectrum $H\underline{M}$ for $G$ a cyclic $p$-group. When $\underline{R}$ is a Green functor, we define orientation classes $u_V$ for…

We define the spine A*(G) of the Fourier-Stieltjes algebra B(G) of a locally compact group G. A*(G) is graded over a certain semi-lattice, that of non-quotient locally precompact topologies on G. We compute the spine's spectrum G*, which…

We answer a question of Schwede on the existence of global Picard spectra associated to his ultra-commutative global ring spectra; given an ultra-commutative global ring spectrum $R$, we show there exists a global spectrum…

Given a global equivariant ultracommutative ring spectrum $E$ and inclusion $H\hookrightarrow G$ of finite groups, one may apply geometric fixed points to the norm $N_H^G E_H \to E_G$ to obtain what we call a \emph{geometric norm} $\Phi^H E…

We show that the abelian monoid of isomorphism classes of G-stable finite S-sets is free for a finite group G with Sylow p-subgroup S; here a finite S-set is called G-stable if it has isomorphic restrictions to G-conjugate subgroups of S.…

We prove new structural results for the rational homotopy type of the classifying space $B\operatorname{aut}(X)$ of fibrations with fiber a simply connected finite CW-complex $X$. We first study nilpotent covers of $B\operatorname{aut}(X)$…

We develop a mechanism of "isotropy separation for compact objects" that explicitly describes an invertible $G$-spectrum through its collection of geometric fixed points and gluing data located in certain variants of the stable module…

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

Let $G$ be a finite group. We re-analyze the splitting of rational $G$-spectra, which is discussed in Barne's thesis and traces back to Greenlees and May. We will study how the splitting behaves under a localization which is weaker than…

We show that the category of $n$-excisive functors from the $\infty$-category of spectra to a target stable $\infty$-category $\mathbf{E}$ is equivalent to the category of $\mathbf{E}$-valued Mackey functors on an indexing category built…

This work concerns representations of a finite flat group scheme $G$, defined over a noetherian commutative ring $R$. The focus is on lattices, namely, finitely generated $G$-modules that are projective as $R$-modules, and on the full…

We introduce support varieties for rational representations of a linear algebraic group $G$ of exponential type over an algebraically closed field $k$ of characteristic $p > 0$. These varieties are closed subspaces of the space $V(G)$ of…

We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring of quotients replaces the classical ring…

We introduce the theory of biset functors defined on finite categories. Previously, biset functors have been defined on groups, and in that context they are closely related to Mackey functors. Standard examples on groups include…