Skip to Main content Skip to Navigation
Theses

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

Abstract : 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 are then used to identify the heart of the Chow weight structure defined by Hébert and Bondarko: it turns out that the heart, namely the category of elements of weight zero, is equivalent to a relative version of pure Chow motives over a base defined by Corti and Hanamura.In the second part we show the representability of Quillen’s G-theory, reformulated by Thomason, firstly in the A1-homotopy category of schemes of Morel-Voevodsky, but also in the stable homotopy category constructed by Jardine. We establish an identification of G-theory as the Borel-Moore theory associated to algebraic K-theory, by using the six functors formalism settled by Ayoub and Cisinski-Déglise.
Document type :
Theses
Complete list of metadata

Cited literature [54 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01420592
Contributor : ABES STAR :  Contact
Submitted on : Tuesday, December 20, 2016 - 5:35:06 PM
Last modification on : Saturday, April 2, 2022 - 3:46:27 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:34:14 AM

File

JIN_Fangzhou_2016LYSEN051_Thes...
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01420592, version 1

Collections

Citation

Fangzhou Jin. On some aspects of Borel-Moore homology in motivic homotopy : weight and Quillen’s G-theory. Algebraic Geometry [math.AG]. Université de Lyon, 2016. English. ⟨NNT : 2016LYSEN051⟩. ⟨tel-01420592⟩

Share

Metrics

Record views

284

Files downloads

146