On the derived category of quasi-coherent sheaves on an Adams geometric stack

Abstract

Let $\mathbf{X}$ be an Adams geometric stack. We show that $D(A_{qc}(\mathbf{X}))$, its derived category of quasi-coherent sheaves, satisfies the axioms of a stable homotopy category defined by Hovey, Palmieri and Strickland. Moreover we show how this structure relates to the derived category of comodules over a Hopf algebroid that determines $\mathbf{X}$.

21 pages, v2 minor additions and corrections

References in corpus (3)

• Tannaka Duality for Geometric Stacks
• Quasi-coherent sheaves on the moduli stack of formal groups
• A characterization of categories of coherent sheaves of certain algebraic stacks

Cited by in corpus (1)

• Perfect complexes on algebraic stacks