Bivariant Theories in Motivic Stable Homotopy
| Autor: | Frédéric Déglise |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
K-Theory and Homology (math.KT) motivic homotopy bivariant theory Mathematics::Algebraic Topology fundamental class orientation Mathematics - Algebraic Geometry 14F42 14F20 19E20 14C40 14F42 (14F20 19E20 14C40) Mathematics::Algebraic Geometry k-theory Mathematics::K-Theory and Homology Mathematics::Category Theory Mathematics - K-Theory and Homology FOS: Mathematics [MATH]Mathematics [math] Algebraic Geometry (math.AG) |
| Zdroj: | Documenta Mathematica Documenta Mathematica, Universität Bielefeld, 2018, 23, pp.997-1076. ⟨10.25537/dm.2018v23.997-1076⟩ |
| ISSN: | 1431-0643 1431-0635 |
| DOI: | 10.25537/dm.2018v23.997-1076⟩ |
| Popis: | The purpose of this work is to study the notion of bivariant theory introduced by Fulton and MacPherson in the context of motivic stable homotopy theory, and more generally in the broader framework of the Grothendieck six functors formalism. We introduce several kinds of bivariant theories associated with a suitable ring spectrum, and we construct a system of orientations (called fundamental classes) for global complete intersection morphisms between arbitrary schemes. These fundamental classes satisfy all the expected properties from classical intersection theory and lead to Gysin morphisms, Riemann-Roch formulas as well asduality statements, valid for general schemes, including singular ones and without need of a base field. Applications are numerous, ranging from classical theories (Betti homology) to generalized theories (algebraic K-theory, algebraic cobordism) and more abstractly to \'etale sheaves (torsion and $l$-adic) and mixed motives. Documenta Mathematica, 2018, vol. 23, p. 997-1076, 1431-0643 |
| Databáze: | OpenAIRE |
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