Affine structures on a ringed space and schemes

Generalized Ringed Spaces and Schemes

Modules over a Ringed Space

In these notes we collect some useful facts about sheaves of modules on a ringed space that are either left as exercises in [Har77] or omitted completely. Most of these observations can be found in [Gro60], which is of course always the best reference. Nonetheless it may be useful for the reader to have an english reference when these points arise in our other notes on algebraic geometry. These...

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...

Poisson Structures on Affine Spaces and Flag Varieties. I. Matrix Affine Poisson Space

The standard Poisson structure on the rectangular matrix variety Mm,n(C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T ⊂ GLm+n(C). These orbits, finite in number, are shown to be smooth irreducible locally closed subvarieties of Mm,n(C), isomorphic to intersections of dual Schubert cells in the full flag variety of GLm+n(C). Three different present...