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Bivariant theories in motivic stable homotopy
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In this article, the authors introduce several kinds of bivariant theory associated with a suitable ring spectrum and construct a system of orientations (called fundamental classes) for global complete intersection morphisms between arbitrary schemes.Abstract:
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 Grothendieck six functors formalism. We introduce several kinds of bivariant theory associated with a suitable ring spectrum and we construct a system of orientations (called fundamental classes) for global complete intersection morphisms between arbitrary schemes. This fundamental classes satisfies all the expected properties from classical intersection theory and lead to Gysin morphisms, Riemann-Roch formulas as well as duality statements, valid for general schemes, including singular ones and without need of a base field.read more
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Fundamental classes in motivic homotopy theory
TL;DR: In this article, the authors develop a theory of fundamental classes in the setting of motivic homotopy theory and construct an associated bivariant theory in the sense of Fulton-MacPherson.
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Virtual fundamental classes of derived stacks I
TL;DR: In this paper, the etale motivic Borel-Moore homology of derived Artin stacks is constructed using a derived version of the intrinsic normal cone and derived classes of quasi-smooth Artin stack and demonstrate functoriality, base change, excess intersection and Grothendieck-Riemann-Roch formulas.
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The Milnor-Witt motivic ring spectrum and its associated theories
Frédéric Déglise,Jean Fasel +1 more
TL;DR: In this article, a ring spectrum representing Milnor-Witt motivic cohomology, as well as its etale local version and three other theories are deduced out of it.
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Framed transfers and motivic fundamental classes
TL;DR: In this paper, the authors compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with $\mathbf P^1$-loop spaces to the theory of motivic fundamental classes of Deglise, Jin, and Khan.
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Bivariant derived algebraic cobordism
TL;DR: In this paper, the derived algebraic bordism of Lowrey and Schurg is extended to a bivariant theory in the sense of Fulton and MacPherson, and some of its basic properties are established.
References
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$A^1$-homotopy theory of schemes
Fabien Morel,Vladimir Voevodsky +1 more
TL;DR: In this article, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of the publication mathématique de l'I.H.É.S.
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Higher Algebraic K-Theory of Schemes and of Derived Categories
R. W. Thomason,Thomas Trobaugh +1 more
TL;DR: In this article, a localization theorem for the K-theory of commutative rings and of schemes is presented, relating the k-groups of a scheme, of an open subscheme, and of those perfect complexes on the scheme which are acyclic on the open scheme.
Journal Article
Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes
TL;DR: In this article, the authors present a legal opinion on the use of commercial or impression systématiques in the context of the publication of books of the I.H.É.S.