Documents  Levine, Marc | enregistrements trouvés : 5

Research talks;Algebraic and Complex Geometry;Topology

After inverting 2, the motivic sphere spectrum splits into a plus part and a minus part with respect to a certain natural involution. Cisinsky and Déglise have shown that, with rational coefficients, the plus part is given by rational motivic cohomlogy. With Ananyevskiy and Panin, we have computed the minus part with rational coefficients as being given by rational Witt-theory. In particular, this shows that the rational bi-graded homotopy sheaves of the minus sphere are concentrated in bi-degree (n,n). This may be rephrased as saying that the graded homotopy sheaves of the minus sphere in strictly positive topological degree are torsion. Combined with the result of Cisinski-Déglise mentioned above, this shows that the graded homotopy sheaves of the sphere spectrum in strictly positive topological degree and non-negative Tate degree are torsion, an analog of the classical theorem of Serre, that the stable homotopy groups of spheres in strictly positive degree are finite. After inverting 2, the motivic sphere spectrum splits into a plus part and a minus part with respect to a certain natural involution. Cisinsky and Déglise have shown that, with rational coefficients, the plus part is given by rational motivic cohomlogy. With Ananyevskiy and Panin, we have computed the minus part with rational coefficients as being given by rational Witt-theory. In particular, this shows that the rational bi-graded homotopy ...

14C25 ; 14F42

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ISBN 978-0-8218-0785-9

Mathematical surveys and monographs , 0057

Localisation : Collection 1er étage

K-théorie # K-théorie de Milnor # K-théorie de dimension supérieure # K-théorie de schéma # anneau d'équivalence rationnelle # cycle et sous-schéma # géométrie # symbole supérieur # théorie d'intersection # théorie de cohomologie # théorème de Riemann-Roch

14C15 ; 14C17 ; 14C25 ; 14C40 ; 19D45 ; 19E08 ; 19E15 ; 19E20

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- 220 p.
ISBN 978-3-540-45895-1

Universitext

Localisation : Ouvrage RdC (Moti)

catégorie modèle # ensemble simplicial # homologie motivique # topologie de Grothendieck

14-XX ; 18-XX ; 19-XX ; 55-XX

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- 244 p.
ISBN 978-3-540-36822-9

Springer monographs in mathematics

Localisation : Ouvrage RdC (LEVI)

cobordisme algébrique # géométrie algébrique # cohomologie # homologie de Borel-Moore # théorème de Quillen # anneau de Lazard # formule de degrée de Rost

14F43 ; 55N22 ; 14C15 ; 14C17 ; 14C40

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