Bivariant theories in motivic stable homotopy

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August undefined, 2024

WebBIVARIANT 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 … 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 ...

32. Bivariant Theories in Motivic Stable Homotopy

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 … Webthe´etale setting (torsion and ℓ-adic coeﬃcients). Besides, thanks to the work of the motivic homotopy community, there are now many examples of such triangulated categories.2 … lwp milton keynes council

Open Problems in the Motivic Stable Homotopy Theory, I

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 … 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 lwp olx

(PDF) Fundamental classes in motivic homotopy theory

WebCohomology theories in algebraic geometry The motivic stable homotopy category Six functors formalism For any scheme X, the triangulated category SH(X) is closed … WebAlgebraic Kasparov K-theory, II Grigory Garkusha A 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. lwp long formMotivic 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 lwpolyline layer

"WebarXiv:1705.01528v2 [math.AG] 10 Sep 2024 BIVARIANT THEORIES IN MOTIVIC STABLE HOMOTOPY FRED´ ERIC D´ ´EGLISE Abstract. The purpose of this work is to study the notion of bivari " - Bivariant theories in motivic stable homotopy

Bivariant theories in motivic stable homotopy

[1705.01528v3] Bivariant theories in motivic stable …

WebMay 3, 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 … 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 …

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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 http://deglise.perso.math.cnrs.fr/docs/2014/beijing.pdf

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. WebMay 3, 2024 · 2 Stable homotopy, mixed motives, modules over ring spectra such as K-theory, algebr aic cobordism. These examples will appear natur ally in the course of the …

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 … 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. …

Webmotivic homotopy theory, after the work of Ayoub ([Ayo07a]), that we became aware of a plain incorporation of bivariant theories into motivic homotopy theory. One can …

WebBivariant Theories in Motivic Stable Homotopy Doc. Math. 23, 997-1076 (2024) DOI: 10.25537/dm.2024v23.997-1076. Summary. 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 ... lwp oldham councilWebstable 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 king snakes of texasWebMotivic stable homotopy and cohomology theories 7 1.3. Absolute purity 9 1.4. Orientation theory: characteristic and fundamental classes 10 ... Motivic categories and bivariant theories 77 3.1. Motivic categories 77 3.1.1. The axiomatic 77 3.1.2. Exceptional functors 84 3.1.3. Relative purity 85 3.2. Borel-Moore homology 85 lwp numberWebthe etale setting (torsion and ‘-adic coe cients). Besides, thanks to the work of the motivic homotopy community, there are now many examples of such triangulated categories.2 Absolute ring spectra and bivariant theories. From classical and motivic homotopy theories, we retain the notion of a ring spectrum but use a version adapted to our theo- king snake yellow and blackWebMar 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 ... king snake vs copperheadWebBesides, thanks to the work of the motivic homotopy community, there are now many examples of such triangulated categories.2 Absolute ring spectra and bivariant … king snatch wheelWebMay 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 … lwp of lol