The intersection complex as a weight truncation and an application to Shimura varieties

TL;DR

This paper introduces a novel perspective on the intersection complex of singular varieties over finite fields, applying it to study the cohomology of noncompact Shimura varieties.

Contribution

It presents a new approach to understanding the intersection complex via weight truncation and applies this to Shimura varieties' cohomology.

Findings

New interpretation of the intersection complex as a weight truncation

Application to cohomology of noncompact Shimura varieties

Potential implications for the study of singular algebraic varieties

Abstract

The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.