Related papers: The $C_2$-effective spectral sequence for $C_2$-eq…

Computation of the K- and KO-theory for the classifying G-spaces for proper actions of certain infinite discrete groups G via a special version of the equivariant Atiyah- Hirzebruch spectral sequence.

We prove the existence of a map of spectra $\tau_A \colon kA \to lA$ between connective topological K-theory and connective algebraic L-theory of a complex $C^*$-algebra A which is natural in A and compatible with multiplicative structures.…

In this paper, we determine the connective K-cohomology with reality of elementary abelian $2$-groups as a module over $\mathbb{Z}[v_1,a]$, where $v_1$ is the equivariant Bott class and $a$ the Euler class of the sign representation. This…

Over any field of characteristic not 2, we establish a 2-term resolution of the $\eta$-periodic, 2-local motivic sphere spectrum by shifts of the connective 2-local Witt K-theory spectrum. This is curiously similar to the resolution of the…

We construct geometric models for classifying spaces of linear algebraic groups in G-equivariant motivic homotopy theory, where G is a tame group scheme. As a consequence, we show that the equivariant motivic spectrum representing the…

If $\Gamma$ is a torsion free $\widetilde A_2$ group acting on an $\widetilde A_2$ building $\Delta$, and $\fk A_{\Gamma}$ is the associated boundary $C^*$-algebra, it is proved that $K_0(\fk A_\Gamma)\otimes \bb R \cong \bb R^{2\beta_2}$,…

We provide a unifying approach to different constructions of the algebraic $K$-theory of equivariant symmetric monoidal categories. A consequence of our work is that every connective genuine $G$-spectrum is equivalent to the equivariant…

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in…

We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories…

We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…

Let $K$ be a number field with ring of integers $\mathcal{O}_K$. We describe and classify finite, flat, and linearly reductive subgroup schemes of $\mathrm{SL}_2$ over $\mathrm{Spec}\:\mathcal{O}_K$. We also establish finiteness results for…

We examine the slice spectral sequence for the cohomology of singular schemes with respect to various motivic T-spectra, especially the motivic cobordism spectrum. When the base field k admits resolution of singularities and X is a scheme…

A 2015 conjecture of Codesido-Grassi-Mari\~no in topological string theory relates the enumerative invariants of toric CY 3-folds to the spectra of operators attached to their mirror curves. We deduce two consequences of this conjecture for…

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…

This is the second part of our series about the Higson-Roe sequence for \'etale groupoids. We devote this part to the proof of the universal $K$-theory surgery exact sequence which extends the seminal results of N. Higson and J. Roe to the…

We develop an Eilenberg-Moore spectral sequence to compute Bredon cohomology of spaces with an action of a group given as a pullback. Using several other spectral sequences, and positive results on the Baum-Connes Conjecture, we are able to…

For X a simply-connected finite H-space, there is a Bousfield-Kan spectral sequence which converges to the homotopy of its K-completion. When X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic homotopy groups in…

We examine a spectral sequence that is naturally associated with the Baum-Connes Conjecture with coefficients for $\mathbb Z^n$ and also constitutes an instance of Kasparov's construction in his work on equivariant $KK$-theory. For $k\leq…

We compute the mod-2 connected KU-homology of the Eilenberg-MacLane space K(Z/2,2), using a novel Adams spectral sequence analysis.

For a separable $C^*$-algebra $A$, we introduce an exact $C^*$-category called the Paschke Category of $A$, which is completely functorial in $A$, and show that its K-theory groups are isomorphic to the topological K-homology groups of the…