Decomposition Theorem for Perverse sheaves on Artin stacks over finite fields

TL;DR

This paper extends the decomposition theorem for perverse sheaves to a broader class of geometric objects called Artin stacks over finite fields, enhancing the theoretical framework of algebraic geometry.

Contribution

It generalizes the decomposition theorem to Artin stacks with affine stabilizers over finite fields, broadening its applicability.

Findings

Decomposition theorem successfully extended to Artin stacks.

Applicable to stacks with affine stabilizers over finite fields.

Provides new tools for algebraic geometry over finite fields.

Abstract

We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.