Related papers: An extended version of additive K-theory

We define an extended Bloch group for an arbitrary field F, and show that this group is canonically isomorphic to K_3^ind(F) if F is a number field. This gives an explicit description of K_3^ind(F) in terms of generators and relations. We…

It is proved that the assembly map in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups $\Gamma$ with finite quotient finite decomposition complexity (a strengthening of finite decomposition…

We construct a version of Beilinson's regulator as a map of sheaves of commutative ring spectra and use it to define a multiplicative variant of differential algebraic K-theory. We use this theory to give an interpretation of Bloch's…

We establish the equivalence of three versions of a finite dimensional quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak $C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an involutive…

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible…

In this paper, we continue our project of defining and studying the infinitesimal versions of the classical, real analytic, invariants of motives. Here, we construct an infinitesimal analog of Bloch's regulator. Let $X/k$ be a scheme of…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

Borel's construction of the regulator gives an injective map from the algebraic $K$-groups of a number field to its Deligne-Beilinson cohomology groups. This has many interesting arithmetic and geometric consequences. The formula for the…

In this paper we consider the Grassmannian complex of projective configurations in weight 2 and 3, and Cathelineau's infinitesimal polylogarithmic complexes. Our main result is a morphism of complexes between the Grassmannian complex and…

For a field $k$ we compute the $K$-theory of the exact category of $k[t_1,\dots,t_n]$-modules that are finite-dimensional over $k$, generalising the work of Kelley and Spanier.

As an attempt to understand motives over $k[x]/(x^m)$, we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. R\"ulling on 0-dimensional cycles. We give an…

We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…

Let $k$ be a field and let $E$ be a finite quiver. We study the structure of the finitely presented modules of finite length over the Leavitt path algebra $L_k (E)$ and show its close relationship with the finite-dimensional representations…

We introduce S-modules, generalizing the notion of Krein $C^*$-modules, where a fixed unitary replaces the symmetry of Krein $C^*$-modules. The representation theory on S-modules is explored and for a given $*$-automorphism $\alpha$ on a…

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for the classifying space for proper actions.…

We study invariants for shifts of finite type obtained as the K-theory of various C*-algebras associated with them. These invariants have been studied intensely over the past thirty years since their introduction by Wolfgang Krieger. They…

Kasparov $KK$-groups $KK(A,B)$ are represented as homotopy groups of the Pedersen-Weibel nonconnective algebraic $K$-theory spectrum of the additive category of Fredholm $(A,B)$-bimodules for $A$ and $B$, respectively, a separable and…

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the…

We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension $F/\mathbb Q_p$, and an arbitrary finite…

Given an element of the Bloch group of a number field~$F$ and a natural number~$n$, we construct an explicit unit in the field $F_n=F(e^{2 \pi i/n})$, well-defined up to $\nn$-th powers of nonzero elements of~$F_n$. The construction uses…