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On the geometric P=W conjecture

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Mauri,  Mirko
Max Planck Institute for Mathematics, Max Planck Society;

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Mazzon,  Enrica
Max Planck Institute for Mathematics, Max Planck Society;

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arXiv:1810.11837.pdf
(Preprint), 575KB

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Citation

Mauri, M., Mazzon, E., & Stevenson, M. (2022). On the geometric P=W conjecture. Selecta Mathematica, 28(3): 65. doi:0.1007/s00029-022-00776-0.


Cite as: http://hdl.handle.net/21.11116/0000-000A-B078-8
Abstract
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 certain character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.