Search results for "Six functors formalism"

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On some aspects of Borel-Moore homology in motivic homotopy : weight and Quillen’s G-theory

2016

The theme of this thesis is different aspects of Borel-Moore theory in the world of motives. Classically, over the field of complex numbers, Borel-Moore homology, also called “homology with compact support”, has some properties quite different from singular homology. In this thesis we study some generalizations and applications of this theory in triangulated categories of motives.The thesis is composed of two parts. In the first part we define Borel-Moore motivic homology in the triangulated categories of mixed motives defined by Cisinski and Déglise and study its various functorial properties, especially a functoriality similar to the refined Gysin morphism defined by Fulton. These results…

Quillen’s K-theory and G-theoryStructure de poidsMixed motives[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Motivic homotopy theoryHomologie de Borel-MooreThéorie de l’homotopie motiviqueMotifs de ChowChow motives[MATH.MATH-KT] Mathematics [math]/K-Theory and Homology [math.KT]G-théorieFormalisme des six foncteursWeight structureSix functors formalismMotifs mixtesRefined Gysin morphismBorel-Moore homologyMorphisme de Gysin raffinéK-théorie de Quillen
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