The perverse filtration for the Hitchin fibration is locally constant

TL;DR

This paper proves that the perverse Leray filtration for the Hitchin fibration remains locally constant in families, supporting the broader $P=W$ conjecture in non-Abelian Hodge theory.

Contribution

It establishes the local constancy of the perverse filtration for the Hitchin fibration, providing evidence for the $P=W$ conjecture.

Findings

Perverse Leray filtration is locally constant in families

Supports the $P=W$ conjecture in non-Abelian Hodge theory

Advances understanding of Hitchin fibration structure

Abstract

We prove that the perverse Leray filtration for the Hitchin morphism is locally constant in families, thus providing some evidence towards the validity of the $P=W$ conjecture due to de Cataldo, Hausel and Migliorini in non Abelian Hodge theory.