Related papers: Derived induction and restriction theory

For a given group $G$ and a collection of subgroups $\mathcal F$ of $G$, we show that there exist a left induced model structure on the category of right $G$-simplicial sets, in which the weak equivalences and cofibrations are the maps that…

Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies partial $\Pi$-property in $G$ if there exists a chief series $\mathit{\Gamma}_G:1=G_0<G_1<\cdots<G_n=G$ of $G$ such that for every $G$-chief factor $G_i/G_{i-1}$ ($1\leq…

Given a finite group G and a G-space X, we show that a direct sum $F_G (X) = \bigoplus_{n \geq 0}K_{G_n} (X^n) \bigotimes \C$ admits a natural graded Hopf algebra and $\lambda$-ring structure, where $G_n$ denotes the wreath product $G \sim…

Suppose that $G$ is a finite group and $H$ is a nilpotent subgroup of $G$. If a character of $H$ induces an irreducible character of $G$, then the generalized Fitting subgroup of $G$ is nilpotent.

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…

Let $\mathbb{G}$ be a split connected reductive group scheme over the ring of integers $\mathfrak{o}$ of a finite extension $L|\mathbb{Q}_p$ and $\lambda\in X(\mathbb{T})$ an algebraic character of a split maximal torus…

We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for $\mathbb{E}_\infty$ ring spectra. In…

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…

We study the geometry of equivariant, proper maps from homogeneous bundles $G\times_P V$ over flag varieties $G/P$ to representations of $G$, called collapsing maps. Kempf showed that, provided the bundle is completely reducible, the image…

For a profinite group $G$ we describe an abelian group $W_G(R; M)$ of $G$-typical Witt vectors with coefficients in an $R$-module $M$ (where $R$ is a commutative ring). This simultaneously generalises the ring $W_G(R)$ of Dress and…

Gersten's injectivity conjecture for a functor $F$ of ``motivic type'', predicts that given a semilocal, ``non-singular'', integral domain $R$ with a fraction field $K$, the restriction morphism induces an injection of $F(R)$ inside $F(K)$.…

We use hypersurface support to classify thick (two-sided) ideals in the stable categories of representations for several families of finite-dimensional integrable Hopf algebras: bosonized quantum complete intersections, quantum Borels in…

Let $G$ be a simply connected Lie group with Lie algebra $\mathfrak{g}$ and denote by $\mathrm{C}_{\bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth…

For a closed Riemannian manifold $M$ with a compact Lie group $G$ acting by isometries, we show that there are infinitely many $G$-invariant minimal hypersurfaces. Under the assumption that $M$ contains at most a finite number of minimal…

Let $G_k$ be a connected reductive algebraic group over an algebraically closed field $k$ of characteristic $\neq 2$. Let $K_k \subset G_k$ be a quasi-split symmetric subgroup of $G_k$ with respect to an involution $\theta_k$ of $G_k$. The…

In this work, we answer the homotopy invariance question for the ''smallest'' non-isotrivial group-scheme over $\mathbb{P}^1$, obtaining a result, which is not contained in previous works due to Knudson and Wendt. More explicitly, let…

Let $G$ be a finite group and $E$ be an $H_\infty$-ring $G$-spectrum. For any $G$-space $X$ and positive integer $m$, we give an explicit description of the smallest Mackey ideal $\underline{J}$ in $\underline{E}^0(X\times B\Sigma_m)$ for…

We extend McClure's results on the restriction maps in equivariant $K$-theory to bivariant $K$-theory: Let $G$ be a compact Lie group and $A$ and $B$ be $G$-$C^*$-algebras. Suppose that $KK^{H}_{n}(A, B)$ is a finitely generated…

We establish an induction isomorphism in the context of measurable bounded cohomology of discrete measured groupoid, which generalizes the Eckmann-Shapiro isomorphism in bounded cohomology of lattices due to Burger and Monod. In our wider…

Let $G$ be a reductive group over a $p$-adic field $F$ of characteristic zero, with $p \gg 0$. In [Kim04], J.-L. Kim studied an equivalence relation called weak associativity on the set of unrefined minimal $K$-types for $G$ in the sense of…