Motivic Homotopy Theory

Abstract

The objective of this thesis is the study of Motivic homotopy theory and Voevodsky’s construction of triangulated category of motives. We will construct a model category called the motivic model category which will be the Bousfield localization of level wise model structure on simplicial presheaves on smooth schemes over a base. As an application of this theory, we will look at the representability results for Nisnevich torsors in Motivic homotopy category. In the second part, we will focus on Voevodsky’s triangulated category of motives. We will define the motivic cohomology and the category of effective motives. Then we will give a brief overview of the relationship between modules over motivic cohomology spectrum and Voevodsky’s category of motives. This provides a relationship between motivic stable homotopy theory and the theory of motives