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 … 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 …

Bivariant theories in motivic stable homotopy

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 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 … thera gloves https://infojaring.com

motivic homotopy theory in nLab

WebMay 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 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 ... http://deglise.perso.math.cnrs.fr/docs/2024/bivariant.pdf the ragman story

A¹ homotopy theory - Wikipedia

Category:Bivariant theory - Wikipedia

Tags:Bivariant theories in motivic stable homotopy

Bivariant theories in motivic stable homotopy

eLibM – Doc. Math. 23, 997-1076 (2024)

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. 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 …

Bivariant theories in motivic stable homotopy

Did you know?

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 … 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 ...

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

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 Webthe 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-

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.

WebMar 17, 2024 · Carlo Mazza, Vladimir Voevodsky and Charles Weibel, Lectures in motivic cohomology (web pdf) As cohomology with coefficients in Eilenberg-Mac Lane objects. … theraglor 90WebThe 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 ragman poemWebOct 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 … signs and symbols rule the worldWebThe 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. the ragman\u0027s daughter 1972WebThe 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 … signs and symbols to indicate dangerWebthe´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 … the ragman companyWebto 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 ... signs and symbols of the catholic church