Related papers: The Milnor-Chow homomorphism revisited

We prove analogues of the fundamental theorem of algebraic K-theory for the second and third homology of SL_2 over an infinite field k. The statements involve Milnor-Witt K-theory and scissors congruence groups. We use these results to…

Given a number field $K$ and an integer $m\geq 0$, let $K_m$ denote the maximal $m$-step solvable Galois extension of $K$ and write $G_K^m$ for the maximal $m$-step solvable Galois group Gal$(K_m/K)$ of $K$. In this paper, we prove that the…

In this work, we present a generalization to varieties and sheaves of the fundamental ideal of the Witt ring of a field by defining a sheaf of fundamental ideals $\tilde{I}$ and a sheaf of Witt rings $\tilde{W}$ in the obvious way. The…

This paper surveys work on generalized Johnson homomorphisms and tools for studying them. The goal is to unite several related threads in the literature and to clarify existing results and relationships among them using Hodge theory. We…

We introduce a metric homotopy theory, which we call Moderately Discontinuous Homotopy, designed to capture Lipschitz properties of metric singular subanalytic germs. It matches with the Moderately Discontinuous Homology theory receantly…

In the paper M. Somekawa, {\it{On Milnor $K$-groups attached at semi-Abelian varieties}}, K-theory, \textbf{4} (1990) p.105, Somekawa conjectures that his Milnor K-group $K(k,G_1,...,G_r)$ attached to semi-abelian varieties $G_1$,...,$G_r$…

Let $n$ be a positive integer, and let $\mathscr{H}_n$ denote the affine KLR algebra in type A. Kleshchev, Mathas and Ram have given a homogeneous presentation for graded column Specht modules $\operatorname{S}_{\lambda}$ for…

Given a non compact semisimple Lie group $G$ we describe all homogeneous spaces $G/L$ carrying an invariant almost K\"ahler structure $(\omega,J)$. When $L$ is abelian and $G$ is of classical type, we classify all such spaces which are…

Let H be a homology theory for algebraic varieties over a field k. To a complete k-variety X, one naturally attaches an ideal of the coefficient ring H(k). We show that, when X is regular, this ideal depends only on the upper Chow motive of…

Given a smooth projective variety $X$ over a field $k$ of characteristic zero, we consider the composition of the de Rham cohomology cycle class map over $k$ from the Chow group $CH^q(X\times_kK)$, where $K$ is the field of fractions of…

We consider the "homotopy coniveau tower" for an arbitrary cohomology theory on smooth varieties over a field or a Dedekind domain. This tower is a generalization of the construction used by Bloch-Lichtenbaum and Friedlander-Suslin in their…

Using algebraic cycles as a medium, we prove that the groups of the big (Hesselholt-Madsen) de Rham-Witt forms over arbitrary fields are isomorphic to the relative improved (Gabber-Kerz) Milnor $K$-groups of Artin local algebras of…

We generalise the Milnor-Schwarz lemma to inverse monoids acting on presheaves of geodesic metric spaces. We provide two proofs of this fact: one only uses elementary techniques, inspired by the arguments for group actions on metric spaces;…

We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an equivariant closed form within its cohomological class to a…

We show that the results of the paper Symplectic Reduction and Riemann-Roch for Circle Actions of Duistermaat, Guillemin, Meinrenken and Wu can be expressed entirely in K-theory. We show that their quantization is simply a pushforward in…

The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

Let A be an approximately subhomogeneous (ASH) C*-algebra with slow dimension growth. We prove that if A is unital and simple, then the Cuntz semigroup of A agrees with that of its tensor product with the Jiang-Su algebra Z. In tandem with…

In this paper we study some new theories of characteristic homology classes for singular complex algebraic varieties. First we introduce a natural transformation T_{y}: K_{0}(var/X) -> H_{*}(X,Q)[y] commuting with proper pushdown, which…

For a quasi-projective smooth scheme X of pure dimension d over a field k and an effective Cartier divisor D on X whose support is a simple normal crossing divisor, we construct a cycle class map from the Chow group of zero-cycles with…