Degenerations and limit Frobenius structures in rigid cohomology
We introduce a 'limiting Frobenius structure' attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be e ectively computable in an appropriate sense for a degene...
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| Format: | Journal article |
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2011
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| _version_ | 1826299844186079232 |
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| author | Lauder, A |
| author_facet | Lauder, A |
| author_sort | Lauder, A |
| collection | OXFORD |
| description | We introduce a 'limiting Frobenius structure' attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be e ectively computable in an appropriate sense for a degeneration of projective hypersurfaces. We conjecture that the limiting Frobenius structure relates to the rigid cohomology of a semistable limit of the degeneration through an analogue of the Clemens-Schmidt exact sequence. Our construction is illustrated, and conjecture supported, by a selection of explicit examples. © 2011 Author. |
| first_indexed | 2024-03-07T05:08:08Z |
| format | Journal article |
| id | oxford-uuid:daa41925-8580-46ac-aed2-5a4e0855fece |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:08:08Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:daa41925-8580-46ac-aed2-5a4e0855fece2022-03-27T09:04:34ZDegenerations and limit Frobenius structures in rigid cohomologyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:daa41925-8580-46ac-aed2-5a4e0855feceSymplectic Elements at Oxford2011Lauder, AWe introduce a 'limiting Frobenius structure' attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be e ectively computable in an appropriate sense for a degeneration of projective hypersurfaces. We conjecture that the limiting Frobenius structure relates to the rigid cohomology of a semistable limit of the degeneration through an analogue of the Clemens-Schmidt exact sequence. Our construction is illustrated, and conjecture supported, by a selection of explicit examples. © 2011 Author. |
| spellingShingle | Lauder, A Degenerations and limit Frobenius structures in rigid cohomology |
| title | Degenerations and limit Frobenius structures in rigid cohomology |
| title_full | Degenerations and limit Frobenius structures in rigid cohomology |
| title_fullStr | Degenerations and limit Frobenius structures in rigid cohomology |
| title_full_unstemmed | Degenerations and limit Frobenius structures in rigid cohomology |
| title_short | Degenerations and limit Frobenius structures in rigid cohomology |
| title_sort | degenerations and limit frobenius structures in rigid cohomology |
| work_keys_str_mv | AT laudera degenerationsandlimitfrobeniusstructuresinrigidcohomology |