Related papers: Hermitian K-theory via oriented Gorenstein algebra…

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…

We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck's six operations. Objects in this category represent generalized cohomology…

We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable $\infty$-category of non-$\mathbb A^1$-invariant motivic spectra, which turns out to be…

Let k be an infinite field. Let R be the semi-local ring of a finite family of closed points on a k-smooth affine irreducible variety, let K be the fraction field of R, and let G be a reductive simple simply connected R-group scheme…

If H is a commutative connected graded Hopf algebra over a commutative ring k, then a certain canonical k-algebra homomorphism H -> H (x) QSym is defined, where QSym denotes the Hopf algebra of quasisymmetric functions over k. This…

A key triviality result for support extension maps for motivic $\mathbb{A}^1$-homotopies of cellular motivic spaces $S$ over a DVR spectrum $B$ is proven. Combining with earlier known results on Gersten complex and the K-theory motivic…

We construct commutative algebra spectra that represent the operator $K$-theory of $C^*$-algebras, which are algebras over the commutative ring spectra that represent topological $K$-theory. The spectral multiplicative structure introduces…

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold $\mathcal{M}$ to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a…

We prove that for every reductive algebraic group $H$ with centre of positive dimension and every integer $K$ there is a smooth and projective variety $X$ and an algebraic $H$-torsor $P \to X$ such that the classifying map $X \to \Bclass H$…

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…

We advance the understanding of K-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K-groups and Witt-groups. By an explicit computation of the slice spectral sequence for higher Witt-theory, we…

We completely characterize genus-0 K-theoretic Gromov-Witten invariants of a compact complex algebraic manifold in terms of cohomological Gromov-Witten invariants of this manifold. This is done by applying (a virtual version of) the…

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the…

Given a smooth projective variety $M$ endowed with a faithful action of a finite group $G$, following Jarvis-Kaufmann-Kimura and Fantechi-G\"ottsche, we define the orbifold motive (or Chen-Ruan motive) of the quotient stack $[M/G]$ as an…

Let $A$ be a graded C*-algebra. We characterize Kasparov's K-theory group $\hat{K}_0(A)$ in terms of graded *-homomorphisms by proving a general converse to the functional calculus theorem for self-adjoint regular operators on graded…

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…

The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then…

We introduce and study a $K$-theory of twisted bundles for associative algebras $A(\mathfrak g)$ of formal series with an infinite-Lie algebra coefficients over arbitrary compact topological spaces. Fibers of such bundles are given by…

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…

We compute the $2$-completed integral motivic homology, effective algebraic K-theory, and very effective hermitian K-theory of the geometric classifying space of the cyclic group of order two over algebraically closed fields, the real…