Bivariant theories in motivic stable homotopy
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 … 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 ...
Bivariant theories in motivic stable homotopy
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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 ... 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 …
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 …
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 … 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
WebarXiv:1705.01528v1 [math.AG] 3 May 2024 BIVARIANT THEORIES IN MOTIVIC STABLE HOMOTOPY FRED´ ERIC D´ ´EGLISE Abstract. The purpose of this work is to study the notion of bivaria
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 … devtech careershttp://deglise.perso.math.cnrs.fr/docs/2014/beijing.pdf church in olympiaWeb4. 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. church in old san juan puerto ricoWebIn 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 … dev tas weatherWebTo 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 ... church in omaha nebraskaWebAlgebraic 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. church in oleyWebCohomology theories in algebraic geometry The motivic stable homotopy category Six functors formalism For any scheme X, the triangulated category SH(X) is closed … church in olney md