Virtual fundamental classes of derived stacks I

2019/09/03 by Khan, Adeel A.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.01332

Abstract

We construct the étale motivic Borel-Moore homology of derived Artin stacks. Using a derived version of the intrinsic normal cone, we construct fundamental classes of quasi-smooth derived Artin stacks and demonstrate functoriality, base change, excess intersection, and Grothendieck-Riemann-Roch formulas. These classes also satisfy a general cohomological Bézout theorem which holds without any transversity hypotheses. The construction is new even for classical stacks and as one application we extend Gabber's proof of the absolute purity conjecture to Artin stacks.

Related

• Cohomology and base change for algebraic stacks
• Virtual fundamental classes, global normal cones and Fulton's canonical classes
• Enhanced six operations and base change theorem for higher Artin stacks
• Flat descent for Artin n-stacks
• Derived smooth stacks and prequantum categories