Abstract. The semi-topological K-theory K ∗ (X) of a quasi-projective complex algebraic variety X is based on the notion of algebraic vector bundles modulo algebraic equivalence. This theory is given… (More)

The semi-topological K-theory of real varieties, KR(−), is an oriented multiplicative (generalized) cohomology theory which extends the authors’ earlier theory, K(−), for complex algebraic varieties.… (More)

We establish the existence of an “Atiyah-Hirzebruch-like” spectral sequence relating the morphic cohomology groups of a smooth, quasi-projective complex variety to its semi-topological K-groups. This… (More)

The semi-topological K-theory of a complex variety was defined in [FW2] with the expectation that it would prove to be a theory lying “part way” between the algebraic K-theory of the variety and the… (More)

We study a promising candidate, due to Grayson, for the \motivic Atiyah-Hirzebruch" spectral sequence associated to a smooth aane variety. We calculate the E 2-terms in a special case and show they… (More)

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t])/K∗(R) in terms of Hochschild homology and the cohomology of… (More)

This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the… (More)

The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a… (More)

We establish the existence of Adams operations on the members of a filtration of K-theory which is defined using products of projective lines. We also show that this filtration induces the gamma… (More)

The morphic Abel-Jacobi map is the analogue of the classical Abel-Jacobi map one obtains by using Lawson and morphic (co)homology in place of the usual singular (co)homology. It thus gives a map from… (More)