Related papers: Motivic Atiyah-Segal completion theorem

This article records multiple results coming from interplay between de-completed topological periodic cyclic homology, Segal conjecture, and F-smoothness. We establish completeness of motivic filtration on de-completed topological periodic…

We provide a calculational method for rational stable equivariant homotopy theory for a torus G based on the homology of the Borel construction on fixed points. More precisely we define an abelian torsion model, A_t(G) of finite injective…

Given a monad T on a suitable enriched category B equipped with a proper factorization system (E,M), we define notions of T-completion, T-closure, and T-density. We show that not only the familiar notions of completion, closure, and density…

The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the…

We are interested in characterising the commutative rings for which a $1$-tilting cotorsion pair $(\mathcal{A}, \mathcal{T})$ provides for covers, that is when the class $\mathcal{A}$ is a covering class. We use Hrbek's bijective…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

We continue the work initiated in arXiv:1206.3645, where we introduced a new stable symmetric monoidal $(\infty,1)$-category $SH_{nc}$ encoding a motivic stable homotopy theory for the noncommutative spaces of Kontsevich and obtained a…

Equivariant $K$-theory is a generalized equivariant cohomology theory which is a hybrid of the $K$-theory of a topological space and the representation theory of the group acting on it. In this article, we review the basics of equivariant…

This paper is concerned with the algebraic K-theory of locally convex algebras stabilized by operator ideals, and its comparison with topological K-theory. We show that the obstruction for the comparison map between algebraic and…

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…

Let (M,\omega,\Phi) be a Hamiltonian T-space and let H be a closed Lie subtorus of T. Under some technical hypotheses on the moment map \Phi, we prove that there is no additive torsion in the integral full orbifold K-theory of the orbifold…

We construct a semi-orthogonal decomposition on the category of perfect complexes on the blow-up of a derived Artin stack in a quasi-smooth centre. This gives a generalization of Thomason's blow-up formula in algebraic K-theory to derived…

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear…

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

It is well-known that algebraic K-theory preserves products of rings. However, in general, algebraic K-theory does not preserve fiber-products of rings, and bi-relative algebraic K-theory measures the deviation. It was proved by Cortinas…

For a Lie group $G$ and a vector bundle $E$ we study those actions of the Lie group $TG$ on $E$ for which the action map $TG\times E \to E$ is a morphism of vector bundles, and call those \emph{affine actions}. We prove that the category…

Using algebraic and topological K-theory together with complex C^*-algebras, we prove that every abelian group may be realized as the centre of a strongly torsion generated group whose integral homology is zero in dimension one and…

Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping…

Let G be a compact Lie group and LG its associated loop group. The main result of this manuscript is a surjectivity theorem from the equivariant K-theory of a Hamiltonian LG-space onto the integral K-theory of its Hamiltonian LG-quotient.…

In this note, we study the $p$-complete topological cyclic homology of the affine line relative to a ring $A$ which is smooth over a perfectoid ring $R$. Denoting by $NTC(A; \mathbb{Z}_p)$ the spectrum which measures the failure of…