ABSTRACT
Motivic homotopy theory was developed by Morel and Voevodsky [64] [69] in the 1990s. The original motivation for the theory was to import homotopical techniques into algebraic geometry. For example, it allowed for the powerful theory of Steenrod operations in algebro-geometric cohomology theories. Motivic homotopy theory was essential to the solution of several long-standing problems in algebraic K-theory, such as the the Milnor conjecture [101] and the Bloch-Kato conjecture [103].
