Semiregularity as a consequence of Goodwillie’s theorem
We realise Buchweitz and Flenner’s semiregularity map (and hence a fortiori Bloch’s semiregularity map) for a smooth variety X as the tangent of a generalised Abel–Jacobi map on the derived moduli stack of perfect complexes on X. The target of this map is an analogue of Deligne cohomology defined in...
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001324/type/journal_article |
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| author | J.P. Pridham |
| author_facet | J.P. Pridham |
| author_sort | J.P. Pridham |
| collection | DOAJ |
| description | We realise Buchweitz and Flenner’s semiregularity map (and hence a fortiori Bloch’s semiregularity map) for a smooth variety X as the tangent of a generalised Abel–Jacobi map on the derived moduli stack of perfect complexes on X. The target of this map is an analogue of Deligne cohomology defined in terms of cyclic homology, and Goodwillie’s theorem on nilpotent ideals ensures that it has the desired tangent space (a truncated de Rham complex). |
| format | Article |
| id | doaj-art-e21030cb4a4d4162a2edd1ccf305a7df |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-e21030cb4a4d4162a2edd1ccf305a7df2025-01-16T21:48:27ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.132Semiregularity as a consequence of Goodwillie’s theoremJ.P. Pridham0https://orcid.org/0009-0005-9537-8747School of Mathematics and Maxwell Institute, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United KingdomWe realise Buchweitz and Flenner’s semiregularity map (and hence a fortiori Bloch’s semiregularity map) for a smooth variety X as the tangent of a generalised Abel–Jacobi map on the derived moduli stack of perfect complexes on X. The target of this map is an analogue of Deligne cohomology defined in terms of cyclic homology, and Goodwillie’s theorem on nilpotent ideals ensures that it has the desired tangent space (a truncated de Rham complex).https://www.cambridge.org/core/product/identifier/S2050509424001324/type/journal_article14B1214A3019L10 |
| spellingShingle | J.P. Pridham Semiregularity as a consequence of Goodwillie’s theorem Forum of Mathematics, Sigma 14B12 14A30 19L10 |
| title | Semiregularity as a consequence of Goodwillie’s theorem |
| title_full | Semiregularity as a consequence of Goodwillie’s theorem |
| title_fullStr | Semiregularity as a consequence of Goodwillie’s theorem |
| title_full_unstemmed | Semiregularity as a consequence of Goodwillie’s theorem |
| title_short | Semiregularity as a consequence of Goodwillie’s theorem |
| title_sort | semiregularity as a consequence of goodwillie s theorem |
| topic | 14B12 14A30 19L10 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001324/type/journal_article |
| work_keys_str_mv | AT jppridham semiregularityasaconsequenceofgoodwilliestheorem |