Related papers: Naive-commutative structure on rational equivarian…

The category of rational G-equivariant cohomology theories for a compact Lie group $G$ is the homotopy category of rational G-spectra and therefore tensor-triangulated. We show that its Balmer spectrum is the set of conjugacy classes of…

We prove structural theorems for computing the completion of a G-spectrum at the augmentation ideal of the Burnside ring of a finite group G. First we show that a G-spectrum can be replaced by a spectrum obtained by allowing only isotropy…

In this paper we give algebraic models for rational G-spectra for a compact Lie group G when the geometric isotropy is restricted to lie in a 1-dimensional block of conjugacy classes. This includes all blocks of all groups of dimension 1,…

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…

In this article we use existing machinery to define connective $K$-theory spectra associated to topological ringoids. Algebraic $K$-theory of discrete ringoids, and the analytic $K$-theory of Banach categories are obtained as special cases.…

We compute the equivariant $K$-theory $K_G^*(G)$ for a simply connected Lie group $G$ (acting on itself by conjugation). We prove that $K_G^*(G)$ is isomorphic to the algebra of Grothendieck differentials on the representation ring. We also…

Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…

We show that algebraic K-theory KGL, the motivic Adams summand ML and their connective covers acquire unique E-infinity structures refining naive multiplicative structures in the motivic stable homotopy category. The proofs combine…

We construct a combinatorially defined involution on the algebraic $K$-theory of the ring spectrum associated to a bimonoidal category with anti-involution. Particular examples of such are braided bimonoidal categories. We investigate…

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…

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 $G$ be a connected reductive algebraic group. Let $\mathcal{E}\rightarrow \mathcal{B}$ be a principal $G\times G$-bundle and $X$ be a regular compactification of $G$. We describe the Grothendieck ring of the associated fibre bundle…

For an arbitrary compact Lie group G, we describe a model for rational G-spectra with toral geometric isotropy and show that there is a convergent Adams spectral sequence based on it. The contribution from geometric isotropy at a subgroup K…

In the Morel-Voevodsky motivic stable homotopy category of a quasi-compact quasi-separated scheme S, several candidates exist for a motivic spectrum representing hermitian K-theory. This note shows that the cellular absolute motivic…

For a finite group $G$, we construct a simplified model for the $G$-symmetric monoidal $G$-$\infty$-category of rational $G$-spectra. Using this model, we classify $\mathcal{I}$-normed algebras in rational $G$-spectra for a given indexing…

For G a complex reductive group and X a smooth projective or convex quasi-projective polarized G-variety we construct a formal map in quantum K-theory from the equivariant quantum K-theory $QK^G(X)$ to the quantum K-theory of the git…

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over…

The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational…

We compare the K-theories of symplectic quotients with respect to a compact connected Lie group and with respect to its maximal torus, and in particular we give a method for computing the former in terms of the latter. More specifically,…

We investigate the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for the algebraic $K$-theory of twisted group rings of a group G with coefficients in a regular ring R or, more…