On the P = W conjecture for SLn

• Mark Andrea de Cataldo ^[1] ; Davesh Maulik ^[2] ; Junliang Shen ^[3]
  1. [1] Stony Brook University

     Stony Brook University

     Town of Brookhaven, Estados Unidos

     
  2. [2] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
  3. [3] Yale University

     Yale University

     Town of New Haven, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 5, 2022
• Idioma: inglés
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• Resumen

  • 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.