Geometric derived Hall algebra

Abstract

We give a geometric formulation of Toën's derived Hall algebra by constructing Grothendieck's six operations for the derived category of lisse-étale constructible sheaves on the derived stacks of complexes. Our formulation is based on an variant of Laszlo and Olsson's theory of derived categories and six operations for algebraic stacks. We also give an $\infty$-theoretic explanation of the theory of derived stacks, which was originally constructed by Toën and Vezzosi in terms of model theoretical language.

102 pages. arXiv admin note: text overlap with arXiv:math/0608040 by other authors

References in corpus (3)

• Higher Topos Theory
• Derived Algebraic Geometry V: Structured Spaces
• Proper local complete intersection morphisms preserve perfect complexes