Moduli of complexes on a proper morphism

Moduli of Complexes on a Proper Morphism

Given a proper morphism X → S, we show that a large class of objects in the derived category of X naturally form an Artin stack locally of finite presentation over S. This class includes S-flat coherent sheaves and, more generally, contains the collection of all S-flat objects which can appear in the heart of a reasonable sheaf of t-structures on X. In this sense, this is the Mother of all Modu...

5 Moduli of complexes on a proper morphism or The mother of all moduli spaces ( of sheaves )

3 Deformation theory of complexes 8 3.1 Statement of the result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Preparations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Complexes over an affine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 The general case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Higher Direct Images of Coherent Sheaves under a Proper Morphism

1.1. Injective resolutions. Let C be an abelian category. An object I ∈ C is injective if the functor Hom(−, I) is exact. An injective resolution of an object A ∈ C is an exact sequence 0→ A→ I → I → . . . where I• are injective. We say C has enough injectives if every object has an injective resolution. It is easy to see that this is equivalent to saying every object can be embedded in an inje...

Chromatic Numbers, Morphism Complexes, and Stiefel-whitney Characteristic Classes

Derived Moduli of Complexes and Derived Grassmannians

In the st part of this paper we construct a model structure for the category of ltered cochain complexes of modules over some commutative ring R and explain how the classical Rees construction relates this to the usual projective model structure over cochain complexes. The second part of the paper is devoted to the study of derived moduli of sheaves: we give a new proof of the representability ...