Resumen de On the P = W conjecture for SLn

Mark Andrea A. de Cataldo, Davesh Maulik, Junliang Shen

• Let p be a prime number. We prove that the P = W conjecture for SLp is equivalent to the P = W conjecture for GLp. As a consequence, we verify the P = W conjecture for genus 2 and SLp. For the proof, we compute the perverse filtration and the weight filtration for the variant cohomology associated with the SLp-Hitchin moduli space and the SLp-twisted character variety, relying on Gröchenig–Wyss–Ziegler’s recent proof of the topological mirror conjecture by Hausel–Thaddeus. Finally we discuss obstructions of studying the cohomology of the SLn-Hitchin moduli space via compact hyper-Kähler manifolds.