Bivariant theories in motivic stable homotopy
WebA kind of motivic stable homotopy theory of algebras is developed. Explicit fibrant replacements for the S1-spectrum and (S1, G)-bispectrum of an algebra are constructed. As an application, unstable, Morita stable and stable universal bivariant theories are recovered. These are shown to be embedded by means of contravariant equivalences as … Web4. The dimensional homotopy t-structure 15 5. The minus A1-derived category and Witt motives 18 6. Rational stable homotopy and Milnor–Witt motives 23 7. SL-Orientations 24 8. Bivariant A1-theory and Chow–Witt groups 28 Appendix A. Continuity in motivic ∞-categories 33 Appendix B. Essentially of finite presentation morphisms 35 B.1.
Bivariant theories in motivic stable homotopy
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WebMar 2, 2015 · motivic cohomology. References. Marc Levine, Mixed Motives, Handbook of K-theory . Denis-Charles Cisinski, Frédéric Déglise, Local and stable homological algebra in Grothendieck abelian categories, arXiv. Section 8.3 of. Alain Connes, Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives WebIn algebraic geometry and algebraic topology, branches of mathematics, A 1 homotopy theory or motivic homotopy theory is a way to apply the techniques of algebraic …
http://deglise.perso.math.cnrs.fr/docs/2015/RR_new.pdf WebThe theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed.
Webstable motivic homotopy theory, thereby obtaining a universal bivariant theory. In order to treat oriented and non-oriented spectra in a single theory, we have to replace Tate twists, as used for example in the Bloch{Ogus axiomatic, by \Thom twists", i.e., twists with respect to vector bundles WebJan 16, 2024 · stable homotopy homology theory is the homology theory represented by the sphere spectrum. ordinary homology is the homology theory represented by an Eilenberg-MacLane spectrum. bordism homology theory is the homology theory represented by a Thom spectrum; Related concepts. generalized cohomology. …
WebThe 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 …
WebThe 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 … china latex bolster pillowWebOct 10, 2024 · 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 … china-latest-free.shpWebMay 15, 2024 · We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sense of Fulton-MacPherson. We import the tools of Fulton's intersection theory into this setting: (refined) Gysin maps, specialization maps, and … grain and cornhttp://deglise.perso.math.cnrs.fr/docs/2024/bivariant.pdf china latex memory foam mattressWebMay 25, 2024 · The stable motivic homotopy category also satisfies the six functors formalism (see [2]). Moreover, it satisfies a suitable uni versal property [ 62 ] and contains the classical theories china latest military news todayWebCohomology theories in algebraic geometry The motivic stable homotopy category Six functors formalism For any scheme X, the triangulated category SH(X) is closed … china latest metal bed designsWebOct 10, 2024 · 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 … china latest news for covid