A Functor to Ringed Spaces

Generalized Ringed Spaces and Schemes

THE FUNCTOR A ON p-LOCAL SPACES

In a previous paper, the authors gave the finest functorial decomposition of the loop suspension of a p-torsion suspension. The purpose of this paper is to generalize this theorem to arbitrary p-local path connected spaces.

Algebroid Prestacks and Deformations of Ringed Spaces

For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules [11] are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. It follows in particular that there is a deformation equivalence between Mod(O) and Qch(O).

On the Cyclic Homology of Ringed Spaces and Schemes

We prove that the cyclic homology of a scheme with an ample line bundle coincides with the cyclic homology of its category of algebraic vector bundles. As a byproduct of the proof, we obtain a new construction of the Chern character of a perfect complex on a ringed space. 1991 Mathematics Subject Classi cation: Primary: 16E40; Secondary: 18E30, 14F05.

On the Cylic Homology of Ringed Spaces and Schemes

In their recent proof [2] of Schapira-Schneider’s conjecture [19], Bressler-Nest-Tsygan construct a (generalized) Chern character from the Ktheory of perfect complexes to the negative cyclic homology HC− ∗ (A) of a sheaf of algebras A on a topological space. The first aim of this paper is to show how to construct a (classical) Chern character defined on the Grothendieck group of perfect complex...