Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric pro...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/128906 |
| _version_ | 1811081656896847872 |
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| author | Feng, Tony L. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Feng, Tony L. |
| author_sort | Feng, Tony L. |
| collection | MIT |
| description | Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for GL[subscript n] over local function fields. This generalizes a theorem of Ngô, who proved the base change fundamental lemma for spherical Hecke algebras for GL[subscript n] over local function fields, and extends to positive characteristic (for GL[subscript n]) a fundamental lemma originally introduced and proved by Haines for p-adic local fields. |
| first_indexed | 2024-09-23T11:50:19Z |
| format | Article |
| id | mit-1721.1/128906 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:50:19Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1289062022-09-27T22:17:31Z Nearby cycles of parahoric shtukas, and a fundamental lemma for base change Feng, Tony L. Massachusetts Institute of Technology. Department of Mathematics Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for GL[subscript n] over local function fields. This generalizes a theorem of Ngô, who proved the base change fundamental lemma for spherical Hecke algebras for GL[subscript n] over local function fields, and extends to positive characteristic (for GL[subscript n]) a fundamental lemma originally introduced and proved by Haines for p-adic local fields. 2020-12-22T22:01:36Z 2020-12-22T22:01:36Z 2020-03 2020-09-24T21:11:39Z Article http://purl.org/eprint/type/JournalArticle 1022-1824 1420-9020 https://hdl.handle.net/1721.1/128906 Feng, Tony. "Nearby cycles of parahoric shtukas, and a fundamental lemma for base change." Selecta Mathematica 26, 2 (March 2020): 21 © 2020 Springer Nature Switzerland AG en https://doi.org/10.1007/s00029-020-0546-z Selecta 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. Springer Nature Switzerland AG application/pdf Springer Science and Business Media LLC Springer International Publishing |
| spellingShingle | Feng, Tony L. Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title | Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title_full | Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title_fullStr | Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title_full_unstemmed | Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title_short | Nearby cycles of parahoric shtukas, and a fundamental lemma for base change |
| title_sort | nearby cycles of parahoric shtukas and a fundamental lemma for base change |
| url | https://hdl.handle.net/1721.1/128906 |
| work_keys_str_mv | AT fengtonyl nearbycyclesofparahoricshtukasandafundamentallemmaforbasechange |