Related papers: Split injectivity of A-theoretic assembly maps

We compute the equivariant complex K-theory ring of a cohomogeneity-one action of a compact Lie group at the level of generators and relations and derive a characterization of K-theoretic equivariant formality for these actions. Less…

Clausen--Scholze introduced the notion of solid spectrum in their condensed mathematics program. We demonstrate that the solidification of algebraic $K$-theory recovers two known constructions: the semitopological $K$-theory of a real…

We use assembly maps to study $\mathbf{TC}(\mathbb{A}[G];p)$, the topological cyclic homology at a prime $p$ of the group algebra of a discrete group $G$ with coefficients in a connective ring spectrum $\mathbb{A}$. For any finite group, we…

We compute the algebraic K-theory modulo p and v_1 of the S-algebra ell/p = k(1), using topological cyclic homology. We use this to compute the homotopy cofiber of a transfer map K(L/p) --> K(L_p), which we interpret as the algebraic…

This submission is a PhD dissertation. It constitutes the summary of the author's work concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. It includes the…

In this paper we study the index theoretic interpretation of the analytical assembly map that appears in the Baum-Connes conjecture. In its general form it may be constructed using Kasparov's equivariant KK-theory. In the special case of a…

We show that for a wide class of manifold pairs N, M satisfying dim(M) = dim(N) + 1, every \pi_1-injective map f : N --> M factorises up to homotopy as a finite cover of an embedding. This result, in the spirit of Waldhausen's torus…

We study algebraic K-theory, syntomic cohomology, and prismatic cohomology of Cartier smooth rings. As an application, we provide an alternative proof of Kelly-Morrow's generalization of the Geisser-Levine theorem computing $p$-adic…

We determine the A(1)-homotopy of the topological cyclic homology of the connective real K-theory spectrum ko. The answer has an associated graded that is a free F_2[v_2^4]-module of rank 52, on explicit generators in stems -1 \le * \le 30.…

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an \'etale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X.…

We classify the primitive idempotents of the $p$-local complex representation ring of a finite group $G$ in terms of the cyclic subgroups of order prime to $p$ and show that they all come from idempotents of the Burnside ring. Our results…

We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…

Let G be a compact Lie group. We build a tower of G-spectra over the suspension spectrum of the space of linear isometries from one G-representation to another. The stable cofibres of the maps running down the tower are certain interesting…

We construct a covariant functor from the topological torus bundles to the so-called Cuntz-Krieger algebras; the functor maps homeomorphic bundles into the stably isomorphic Cuntz-Krieger algebras. It is shown, that the K-theory of the…

We construct a theory of motivic cohomology for quasi-compact, quasi-separated schemes of equal characteristic, which is related to non-connective algebraic $K$-theory via an Atiyah--Hirzebruch spectral sequence, and to \'etale cohomology…

We give a new construction of the equivariant $K$-theory of group actions (cf. Barwick et al.), producing an infinite loop $G$-space for each Waldhausen category with $G$-action, for a finite group $G$. On the category $R(X)$ of retractive…

We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is based on the use of geometric deformation…

We formulate analogues, for Noetherian local $\mathbb Q$-algebras which are not necessarily regular, of the injectivity part of Gersten's conjecture in algebraic $K$-theory, and prove them in various cases. Our results suggest that the…

We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence…

C. Weibel and Thomason-Trobaugh proved (under some assumptions) that algebraic K-theory with coefficients is A1-homotopy invariant. In this article we generalize this result from schemes to the broad setting of dg categories. Along the way,…