Bivariant theories in motivic stable homotopy

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August undefined, 2024

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. 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 …

Cycles, Transfers and Motivic Homology Theories - Google Books

WebFeb 25, 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 … 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 … how many marched on bloody sunday

BIVARIANT THEORIES IN MOTIVIC STABLE HOMOTOPY

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 Webto build E out of motivic Eilenberg-MacLane spectra by looking at the mo-tivic homotopy groups of E. There is a spectral sequence which starts with cohomology with coeﬃcients in the sheaves of motivic homotopy groups of E and converges to the theory represented by E but the cohomology with coeﬃcients in the sheaves of homotopy groups are ... WebThe stable motivic homotopy category also satisﬁes the six functors formalism (see [2]). ... Fundamental classes in motivic homotopy theory 3937 the bivariant theories of Fulton and MacPherson [34]. The key element of these axio-matizations was the notion of the fundamental class, which was used to express duality ... how many marched on washington in 1963

Cohomology theories in motivic stable homotopy theory

WebMar 22, 2024 · Bivariant Theories in Motivic Stable Homotopy. Article. Full-text available. May 2024; DOC MATH; Frédéric Déglise; The purpose of this work is to study the notion of bivariant theory introduced ... Webto build E out of motivic Eilenberg-MacLane spectra by looking at the mo-tivic homotopy groups of E. There is a spectral sequence which starts with cohomology with coeﬃcients … how are fireworks made ks2WebOct 26, 2024 · Bivariant theories in motivic stable homotopy. Jan 2024; DOC MATH; 997-1076, Bivariant theories in motivic stable homotopy, Doc. Math. 23 (2024), 997-1076. how are fireworks colored

"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

Bivariant theories in motivic stable homotopy

http://deglise.perso.math.cnrs.fr/docs/2015/RR_new.pdf WebMay 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 …

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Motivic homotopy theory or A1-homotopy theory is the homotopy theory of smooth schemes, where the affine line A1 plays the role of the interval. Hence what is called the motivic homotopy category or the 𝔸1-homotopy category bears the same relation to smooth varieties that the ordinary homotopy category … See more Let S be a fixed Noetherian base scheme, and let Sm/S be the category of smooth schemes of finite type over S. Thus, a motivic space over S is an (∞,1)-presheaf F on Sm/Ssuch that 1. F is an (∞,1)-sheaf for the Nisnevich … See more A general theory of equivariant (unstable and stable) motivic homotopy theory was introduced in (Carlsson-Joshua 2014) and further developed in (Hoyois 15). See more Thus, a motivic spectrum E is a sequence of pointed motivic spaces (E0,E1,E2…) together with equivalences Since T≃ℙ1, we could … See more Webis a Serre ﬁbration of topological spaces, where B has the homotopy type of a (connected) ﬁnite CW complex, and E is a (generalized) cohomology theory in the sense of classical stable homotopy theory. One may consider an associated Atiyah–Hirzebruchspectralsequence(see,e.g.,[DK01,§9.2-9.5]): theE 2-pageof

WebTo do this, we rst introduce the fundamentals of motivic homotopy theory, constructing and examining the stable motivic homotopy category which is the general object of study. We then interrogate the analogy between mo-tivic spaces and topological spaces by examining the class of cellular motivic spaces, the appropriate motivic analog of CW ... WebMay 3, 2024 · Bivariant theories in motivic stable homotopy. F. Déglise. The purpose of this work is to study the notion of bivariant theory introduced by Fulton and …

WebBesides, thanks to the work of the motivic homotopy community, there are now many examples of such triangulated categories.2 Absolute ring spectra and bivariant …

WebOct 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 … how are fireworks made step by stepWebMay 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 how are fireworks used todayWebThe 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 … how are fireworks made chemistryWebBIVARIANT THEORIES IN MOTIVIC STABLE HOMOTOPY 7 The same thing works for cohomology with compact support but for ho-mology, we only get an exterior product. It … how many marches did martin luther king leadWebIn mathematics, a bivariant theory was introduced by Fulton and MacPherson (Fulton & MacPherson 1981), in order to put a ring structure on the Chow group of a singular … how many marched from selma to montgomeryWebCohomology theories in algebraic geometry The motivic stable homotopy category Six functors formalism For any scheme X, the triangulated category SH(X) is closed … how are fish and dogs relatedWeb∗,⋆1hold in every other theory representable in the stable motivic homotopy category, such as algebraic cobordism, algebraic and hermitian K-theory, motivic cohomology, and higher Witt theory. In an influential result, Morel identified the endomorphism ring of the motivic sphere with the Grothendieck-Witt ring GW(F)that encodes the how are fire zones identified