On the geometric P=W conjecture
Algebraic Geometry
2022-05-18 v4
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.
Cite
@article{arxiv.1810.11837,
title = {On the geometric P=W conjecture},
author = {Mirko Mauri and Enrica Mazzon and Matthew Stevenson},
journal= {arXiv preprint arXiv:1810.11837},
year = {2022}
}
Comments
33 pages. New appendix. Other minor changes. Final version in Selecta Mathematica