Category-valued sheaves

Constructible Sheaves and the Fukaya Category

Let X be a compact real analytic manifold, and let T ∗X be its cotangent bundle. Let Sh(X) be the triangulated dg category of bounded, constructible complexes of sheaves on X. In this paper, we develop a Fukaya A∞-category Fuk(T ∗X) whose objects are exact, not necessarily compact Lagrangian branes in the cotangent bundle. We write TwFuk(T ∗X) for the A∞-triangulated envelope of Fuk(T ∗X) consi...

Model Category Structures on Chain Complexes of Sheaves

In this paper, we try to determine when the derived category of an abelian category is the homotopy category of a model structure on the category of chain complexes. We prove that this is always the case when the abelian category is a Grothendieck category, as has also been done by Morel. But this model structure is not very useful for defining derived tensor products. We therefore consider ano...

Building a Model Category out of Multiplier Ideal Sheaves

We will construct a Quillen model structure out of the multiplier ideal sheaves on a smooth quasi-projective variety using earlier works of Isaksen and Barnea and Schlank. We also show that fibrant objects of this model category are made of kawamata log terminal pairs in birational geometry.

On the Derived Category of Sheaves on a Manifold

Let M be a non–compact, connected manifold of dimension ≥ 1. Let D(sheaves/M) be the unbounded derived category of chain complexes of sheaves of abelian groups on M . We prove that D(sheaves/M) is not a compactly generated triangulated category, but is well generated. 2000 Mathematics Subject Classification: 18E30 55P99 55U35

Ultrapowers as sheaves on a category of ultrafilters