Related papers: Derived induction and restriction theory

Let $G$ be a finite group and let $\mathscr{F}$ be a family of subgroups of $G$. We introduce a class of $G$-equivariant spectra that we call $\mathscr{F}$-nilpotent. This definition fits into the general theory of torsion, complete, and…

Let G be a compact Lie group. We present two induction theorems for certain generalized G-equivariant cohomology theories. The theory applies to G-equivariant K-theory K_G, and to the Borel cohomology associated to any complex oriented…

Let $k$ be a number field and $G$ be a finite group. Let $\mathfrak{F}_{k}^{G}(Q)$ be the family of number fields $K$ with absolute discriminant $D_K$ at most $Q$ such that $K/k$ is normal with Galois group isomorphic to $G$. If $G$ is the…

We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all…

Let $G$ be a finite group acting on a small category $I$. We study functors $X \colon I \to \mathscr{C}$ equipped with families of compatible natural transformations that give a kind of generalized $G$-action on $X$. Such objects are called…

For $G$ a connected, reductive group over an algebraically closed field $k$ of large characteristic, we use the canonical Springer isomorphism between the nilpotent variety of $\mathfrak{g}:=\mathrm{Lie}(G)$ and the unipotent variety of $G$…

We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as…

The uniform $\mathcal{F}_p$-isomorphism theorem of Quillen gives a comparison map between the Borel equivariant $\mathbf{Z}/p$-cohomology of a space and a limit involving only the Borel equivariant cohomology groups of the same space with…

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…

The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K- and L-theory of the group ring and the topological K-theory of the reduced group C^*-algebra of a group G in terms of these functors for the…

Let $G$ be a group and let $E$ be a functor from small $\Z$-linear categories to spectra. Also let $A$ be a ring with a $G$-action. Under mild conditions on $E$ and $A$ one can define an equivariant homology theory of $G$-simplicial sets…

Let F be a field, let G be its absolute Galois group, and let R(G, k) be the representation ring of G over a suitable field k. In this preprint we construct a ring homomorphism from the mod 2 Milnor K-theory k_*(F) to the graded ring gr…

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 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…

We extend the theory of holomorphic induction of unitary representations of a possibly infinite-dimensional Lie group $G$ beyond the setting where the representation being induced is required to be norm-continuous. We allow the group $G$ to…

We prove an induction theorem for the higher algebraic K-groups of group algebras $kG$ of finite groups $G$ over characteristic $p$ finite fields $k$. For a certain class of finite groups, which we call $p$-isolated, this reduces…

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result…

Let $\mathcal{G}$ be a smooth linear group scheme of finite type. For any positive integer $k$ and a finite field $\mathbb{F}$, let $W_k(\mathbb{F})$ be the ring of Witt vectors of length $k$ over $\mathbb{F}$. We show that the group…

In this paper we develop the definition of a global orthogonal spectrum and its unitary version. It relates $G-$equivariant spectra by equivariant weak equivalence in a coherent way. This category of global spectra has a model structure…

We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories…