Nonabelian Hodge theory for stacks and a stacky P=W conjecture

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Abstract / Description of output

We introduce a version of the P=W conjecture relating the Borel–Moore homology of the stack of representations of the fundamental group of a genus gRiemann surface with the Borel–Moore homology of the stack of degree zero semistable Higgs bundles on a smooth projective complex curve of genus g. In order to state the conjecture we propose a construction of a canonical isomorphism between these Borel–Moore homology groups. We relate the stacky P=W conjecture with the original P=W conjecture concerning the cohomology of smooth moduli spaces, and the PI=WI conjecture concerning the intersection cohomology groups of singular moduli spaces. In genus zero and one, we prove the conjectures that we introduce in this paper.
Original languageEnglish
Article number108889
JournalAdvances in Mathematics
Volume415
Early online date2 Feb 2023
DOIs
Publication statusPublished - 15 Feb 2023

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