Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture
We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2016
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| Online Access: | http://hdl.handle.net/1721.1/103062 https://orcid.org/0000-0002-9302-7354 |
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| author | Achar, Pramod N. Rider, Laura |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Achar, Pramod N. Rider, Laura |
| author_sort | Achar, Pramod N. |
| collection | MIT |
| description | We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau–Mautner–Williamson theory of parity sheaves. |
| first_indexed | 2024-09-23T09:49:36Z |
| format | Article |
| id | mit-1721.1/103062 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:49:36Z |
| publishDate | 2016 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1030622022-09-26T13:59:40Z Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture Achar, Pramod N. Rider, Laura Massachusetts Institute of Technology. Department of Mathematics Rider, Laura We prove the Mirković–Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau–Mautner–Williamson theory of parity sheaves. National Science Foundation (U.S.) (NSF Grant No. DMS-1001594) National Science Foundation (U.S.) (NSF postdoctoral research fellowship) 2016-06-08T18:52:55Z 2017-03-01T16:14:49Z 2016-02 2015-12 2016-05-23T12:08:21Z Article http://purl.org/eprint/type/JournalArticle 0001-5962 1871-2509 http://hdl.handle.net/1721.1/103062 Achar, Pramod N., and Laura Rider. “Parity Sheaves on the Affine Grassmannian and the Mirković–Vilonen Conjecture.” Acta Math 215, no. 2 (December 2015): 183–216. https://orcid.org/0000-0002-9302-7354 en http://dx.doi.org/10.1007/s11511-016-0132-6 Acta Mathematica Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Institut Mittag-Leffler application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Achar, Pramod N. Rider, Laura Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title | Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title_full | Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title_fullStr | Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title_full_unstemmed | Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title_short | Parity sheaves on the affine Grassmannian and the Mirković–Vilonen conjecture |
| title_sort | parity sheaves on the affine grassmannian and the mirkovic vilonen conjecture |
| url | http://hdl.handle.net/1721.1/103062 https://orcid.org/0000-0002-9302-7354 |
| work_keys_str_mv | AT acharpramodn paritysheavesontheaffinegrassmannianandthemirkovicvilonenconjecture AT riderlaura paritysheavesontheaffinegrassmannianandthemirkovicvilonenconjecture |