We introduce a generalization of the Atiyah-Drinfeld-Hitchin-Manin linear algebraic data and a generalization of Atiyah-Drinfeld-Hitchin-Manin equation, which are subsequently used to construct all framed instanton bundles on complex projective spaces. Using geometric invariant theory, we prove that the moduli spaces of framed instanton sheaves is a quasiprojective variety. We also provide a li...

We apply the machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow groups of classifying spaces constructed by Totaro and generalized to arbitrary X by Edidin-Graham) and an AtiyahHirzebruch spectral sequence f...

The purpose of this paper is to verify a conjecture Gross under mild hypotheses: all reduced, separated, and excellent schemes have the resolution property away from closed subset codimension ≥ 3<...

Sheaf theoretic notions and methods have entered model theory during recent years and important constructions like reduced powers and products, unions of chains, Boolean valued models and models for non-classical logics appear here in a unified setting. If one looks at a sheaf as a generalized structure, then forcing becomes the genuine extension of the validity relation between models and form...