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Triangulated categories of logarithmic motives over a field
In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log schemes, and the basic idea of parameterizing homotopies by , i.e...
| Auteurs principaux : | , , |
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| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Triangulated categories of logarithmic motives over a field / Federico Binda, Doosung Park & Paul Arne Østvær |
| Publié : |
Paris :
Société mathématique de France
, C 2022 |
| Description matérielle : | 1 vol. (ix-267 p.) |
| Collection : | Astérisque ; 433 |
| Sujets : | |
| Documents associés : | Autre format:
Triangulated categories of logarithmic motives over a field Fait partie de l'ensemble: Astérisque |
| Résumé : | In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the dividing Nisnevich topology on log schemes, and the basic idea of parameterizing homotopies by , i.e. the projective line with respect to its compactifying logarithmic structure at infinity. We show that Hodge cohomology of log schemes is a -invariant theory that is representable in the category of logarithmic motives. Our category is closely related to Voevodsky's category of motives and A1-invariant theories: assuming resolution of singularities, we identify the latter with the full subcategory comprised of A1-local objects in the category of logarithmic motives. Fundamental properties such as -homotopy invariance, Mayer-Vietoris for coverings, the analogs of the Gysin sequence and the Thom space isomorphism as well as a blow-up formula and a projective bundle formula witness the robustness of the setup. |
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| Notes : | Résumé en anglais et en français |
| Historique des publications : | N° de : "Astérisque", ISSN 0303-1179, (2022)n°433 |
| Bibliographie : | Bibliographie p. [257]-263. Index |
| ISBN : | 978-2-85629-957-9 |