| Softcover ISBN: | 978-2-85629-957-9 |
| Product Code: | AST/433 |
| List Price: | $82.00 |
| AMS Member Price: | $65.60 |
| Softcover ISBN: | 978-2-85629-957-9 |
| Product Code: | AST/433 |
| List Price: | $82.00 |
| AMS Member Price: | $65.60 |
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Book DetailsAstérisqueVolume: 433; 2022; 280 ppMSC: Primary 14; 18; 19
In this work the authors develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. The authors' 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 \(\overline\square \), i.e., the projective line with respect to its compactifying logarithmic structure at infinity. The authors show that Hodge cohomology of log schemes is a \(\overline\square\)-invariant theory that is representable in the category of logarithmic motives. Their category is closely related to Voevodsky's category of motives and \(\mathbb{A}^{1}\)-invariant theories: assuming resolution of singularities, the authors identify the latter with the full subcategory comprised of \(\mathbb{A}^{1}\)-local objects in the category of logarithmic motives. Fundamental properties such as \(\overline\square\)-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.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
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In this work the authors develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. The authors' 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 \(\overline\square \), i.e., the projective line with respect to its compactifying logarithmic structure at infinity. The authors show that Hodge cohomology of log schemes is a \(\overline\square\)-invariant theory that is representable in the category of logarithmic motives. Their category is closely related to Voevodsky's category of motives and \(\mathbb{A}^{1}\)-invariant theories: assuming resolution of singularities, the authors identify the latter with the full subcategory comprised of \(\mathbb{A}^{1}\)-local objects in the category of logarithmic motives. Fundamental properties such as \(\overline\square\)-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.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
