Exterior Power Operations on Higher K-groups via Binary Complexes

Exterior Power Operations on Higher K-theory

A Hochschild-cyclic Approach to Additive Higher Chow Cycles

Over a field of characteristic zero, we introduce two motivic operations on additive higher Chow cycles: analogues of the Connes boundary B operator and the shuffle product on Hochschild complexes. The former allows us to apply the formalism of mixed complexes to additive Chow complexes building a bridge between additive higher Chow theory and additive K-theory. The latter induces a wedge produ...

A Chain Morphism for Adams Operations on Rational Algebraic K-theory

For any regular noetherian scheme X and every k ≥ 1, we define a chain morphism Ψ between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by Q. It is shown that the morphisms Ψ induce in homology the Adams operations defined by Gillet and Soulé or the ones defined by Grayson. Introduction Let X be any scheme and let P(X) be the...

Algebraic proofs of some fundamental theorems in algebraic K - theory

We present new proofs of the additivity, resolution and cofinality theorems for the algebraic K-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic K-groups via binary complexes. 2000 Mathematics Subject Classification: 19D99

On p-minimal homological models of twisted tensor products of elementary complexes localised over a prime

In this paper, working over Z(p) and using algebra perturbation results from [18], p-minimal homological models of twisted tensor products (TTPs) of Cartan’s elementary complexes are obtained. Moreover, making use of the notion of indecomposability of a TTP, we deduce that a homological model of a indecomposable p-minimal TTP of length ` (` ≥ 2) of exterior and divided power algebras is a tenso...