Generic Base Change, Artin's Comparison Theorem, and the Decomposition Theorem for Complex Artin stacks

TL;DR

This paper establishes a generic base change theorem for stacks, explores comparison theorems between derived categories of complex analytic stacks, and extends the decomposition theorem for perverse sheaves to complex Artin stacks with affine stabilizers.

Contribution

It introduces a generic base change theorem for stacks and connects derived categories of complex analytic stacks to finite field cases, enabling new decomposition results.

Findings

Proved the generic base change theorem for stacks.

Established comparison theorems between derived categories of complex analytic stacks.

Extended the decomposition theorem for perverse sheaves to complex Artin stacks with affine stabilizers.

Abstract

We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables us to deduce the decomposition theorem for perverse sheaves on complex Artin stacks with affine stabilizers from the case over finite fields.