On the geometric P=W conjecture

Mirko Mauri; Enrica Mazzon; Matthew Stevenson

doi:10.1007/s00029-022-00776-0

On the geometric P=W conjecture

Mirko Mauri
, Enrica Mazzon
, Matthew Stevenson

University of Michigan, Ann Arbor

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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 character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.

Original language	English
Article number	65
Journal	Selecta Mathematica, New Series
Volume	28
Issue number	3
DOIs	https://doi.org/10.1007/s00029-022-00776-0
Publication status	Published - 1 Jul 2022
Externally published	Yes

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title = "On the geometric P=W conjecture",

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 character varieties. We also clarify the relation between the geometric and the cohomological P=W conjectures.",

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AU - Mazzon, Enrica

AU - Stevenson, Matthew

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AB - 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.

UR - https://www.scopus.com/pages/publications/85129717801

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DO - 10.1007/s00029-022-00776-0

M3 - Article

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VL - 28

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

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On the geometric P=W conjecture

Abstract

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