Motivic action on coherent cohomology of Hilbert modular varieties
We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo p and over C, and we conjecture that they both lift to an action on...
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| Format: | Journal article |
| Language: | English |
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Oxford University Press
2022
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| _version_ | 1797111486056759296 |
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| author | Horawa, A |
| author_facet | Horawa, A |
| author_sort | Horawa, A |
| collection | OXFORD |
| description | We propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo p and over C, and we conjecture that they both lift to an action on cohomology with integral coefficients. The conjecture is supported by theoretical evidence based on Stark’s conjecture on special values of Artin L-functions and by numerical evidence in base change cases. |
| first_indexed | 2024-03-07T08:11:06Z |
| format | Journal article |
| id | oxford-uuid:6a9da20d-fc50-4580-a0b3-299aa52c84e5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:11:06Z |
| publishDate | 2022 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:6a9da20d-fc50-4580-a0b3-299aa52c84e52023-11-28T08:23:53ZMotivic action on coherent cohomology of Hilbert modular varietiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6a9da20d-fc50-4580-a0b3-299aa52c84e5EnglishSymplectic ElementsOxford University Press2022Horawa, AWe propose an action of a certain motivic cohomology group on the coherent cohomology of Hilbert modular varieties, extending conjectures of Venkatesh, Prasanna, and Harris. The action is described in two ways: on cohomology modulo p and over C, and we conjecture that they both lift to an action on cohomology with integral coefficients. The conjecture is supported by theoretical evidence based on Stark’s conjecture on special values of Artin L-functions and by numerical evidence in base change cases. |
| spellingShingle | Horawa, A Motivic action on coherent cohomology of Hilbert modular varieties |
| title | Motivic action on coherent cohomology of Hilbert modular varieties |
| title_full | Motivic action on coherent cohomology of Hilbert modular varieties |
| title_fullStr | Motivic action on coherent cohomology of Hilbert modular varieties |
| title_full_unstemmed | Motivic action on coherent cohomology of Hilbert modular varieties |
| title_short | Motivic action on coherent cohomology of Hilbert modular varieties |
| title_sort | motivic action on coherent cohomology of hilbert modular varieties |
| work_keys_str_mv | AT horawaa motivicactiononcoherentcohomologyofhilbertmodularvarieties |