Stable Configurations of Linear Subspaces and Quotient Coherent Sheaves

Descent of Coherent Sheaves and Complexes to Geometric Invariant Theory Quotients

Fix a quasi-projective scheme X over a field of characteristic zero that is equipped with an action of a reductive algebraic group G. Fix a polarization H of X that linearizes the G-action. We give necessary and sufficient conditions for a G-equivariant coherent sheaf on X to descend to the GIT quotient X/G, or for a bounded-above complex of G-equivariant coherent sheaves on X to be G-equivaria...

Descent of Coherent Sheaves and Complexes to Geometric Invariant Theory Quotients: Draft

Fix a quasi-projective scheme X over a field of characteristic zero that is equipped with an action of a reductive algebraic group G. Fix a polarization H of X that linearizes the G-action. We give necessary and sufficient conditions for a G-equivariant coherent sheaf on X to descend to the GIT quotient X/G, or for a bounded-above complex of G-equivariant coherent sheaves on X to be G-equivaria...

Cohomology of Coherent Sheaves and Series of Supernatural Bundles

We show that the cohomology table of any coherent sheaf on projective space is a convergent—but possibly infinite—sum of positive real multiples of the cohomology tables of what we call supernatural sheaves. Introduction Let K be a field, and let F be a coherent sheaf on P = P K . The cohomology table of F is the collection of numbers γ(F) = (γi,d) with γi,d = dimH (P,F(d)), which we think of a...

ε-weakly Chebyshev subspaces and quotient spaces

The Stable Derived Category of a Noetherian Scheme

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect complexes. Some applications are included, for instance an analogue of maximal CohenMacaulay approximations, a construction of Tate cohomology, and an extension ...