On the geometric P=W conjecture

Mirko Mauri ^[1] ; Enrica Mazzon ^[1] ; Matthew Stevenson ^[1]
1. [1] University of Michigan–Ann Arbor
  
  University of Michigan–Ann Arbor
  
  City of Ann Arbor, Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022, 45 págs.
Idioma: inglés
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Resumen
- We formulate the geometric P=W conjecture for singular character varieties. We establish it for compact Riemann surfaces of genus one, and obtain partial results in arbitrary genus. To this end, we employ non-Archimedean, birational and degeneration techniques to study the topology of the dual boundary complex of character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.