On the geometric P=W conjecture

On the geometric P=W conjecture

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 bound...

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Veröffentlicht in:Selecta mathematica (Basel, Switzerland) Switzerland), 2022-07, Vol.28 (3), Article 65
Hauptverfasser: Mauri, Mirko, Mazzon, Enrica, Stevenson, Matthew
Format: Artikel
Sprache:eng
Schlagworte:
Degeneration
Mathematics
Mathematics and Statistics
Riemann surfaces
Topology
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Zusammenfassung: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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-022-00776-0