  Motivic homotopy theory is meant to play the role of algebraic topology, in
particular homotopy theory, in the context of algebraic geometry. As proved by
Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to
Voevodsky's triangulated category of motives. A connection that is the motivic
analogue of the connection between algebraic topology and homological algebra.
In this paper, we try to understand the big picture of motivic homotopy theory
and its connection to Voevodsky's motives by comparison to the classical
counterpart.

Algebraic Geometry;Algebraic Topology