Adjoint Pairs for Quasi-coherent Sheaves on Stacks
نویسنده
چکیده
In this paper we construct a pushforward-pullback adjoint pair for categories of quasi-coherent sheaves, along a morphism of algebraic stacks, which is represented in algebraic stacks over the site C = Affflat. The construction uses the characterization of algebraic stacks of [H3] and is based on the descent description of the category of quasi-coherent sheaves given in [H2]. We show that an essentially immediate consequence of the presentation we give for this adjoint pair is the Miller-Ravenel-Morava change of rings theorem and the algebraic chromatic convergence theorem.
منابع مشابه
Descent for Quasi-coherent Sheaves on Stacks
We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.
متن کاملSheaves on Artin Stacks
We develop a theory of quasi–coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of Laumon and Moret-Bailly. We study basic cohomological properties of such sheaves, and prove stack–theoretic versions of Grothendieck’s Fundamental Theorem for proper morphisms, Grothendieck’s Existence Theorem, Zariski’s Connectedness Theorem, as well as finiteness Theo...
متن کاملDerived Algebraic Geometry VIII: Quasi-Coherent Sheaves and Tannaka Duality Theorems
1 Generalities on Spectral Deligne-Mumford Stacks 4 1.1 Points of Spectral Deligne-Mumford Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Étale Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Localic Spectral Deligne-Mumford Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 Quasi-Compactness of Sp...
متن کاملWrong Way Recollement for Schemes
Here X is a topological space equal to the union of the closed subset Z and the open complement U , and D(Z), D(X), and D(U) are suitable derived categories of sheaves. The triangulated functors in a recollement must satisfy various conditions, most importantly that (i, i∗), (i∗, i ), (j!, j ), and (j, j∗) are adjoint pairs. The purpose of this note is to point out that, somewhat surprisingly, ...
متن کاملDerived Categories of Stacks
In this chapter we write about derived categories associated to algebraic stacks. This means in particular derived categories of quasi-coherent sheaves, i.e., we prove analogues of the results on schemes (see Derived Categories of Schemes, Section 1) and algebraic spaces (see Derived Categories of Spaces, Section 1). The results in this chapter are different from those in [LMB00] mainly because...
متن کامل