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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2112.10830 |
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| _version_ | 1866913298875678720 |
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| author | Davison, Ben |
| author_facet | Davison, Ben |
| contents | 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 g Riemann 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 of twisted objects, and the PI=WI conjecture concerning the intersection cohomology groups of singular moduli spaces of untwisted objects. In genus zero and one, we prove the conjectures that we introduce in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10830 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonabelian Hodge theory for stacks and a stacky P=W conjecture Davison, Ben Algebraic Geometry High Energy Physics - Theory Representation Theory 14F08, 14D20 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 g Riemann 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 of twisted objects, and the PI=WI conjecture concerning the intersection cohomology groups of singular moduli spaces of untwisted objects. In genus zero and one, we prove the conjectures that we introduce in this paper. |
| title | Nonabelian Hodge theory for stacks and a stacky P=W conjecture |
| topic | Algebraic Geometry High Energy Physics - Theory Representation Theory 14F08, 14D20 |
| url | https://arxiv.org/abs/2112.10830 |