Motivic Homotopy Theory

Abstract

We give an informal discussion of the roots and accomplishments of motivic homotopy theory. Mathematics Subject Classification (2000). 14F45, 55P43.

A primer for unstable motivic homotopy theory

“…As mentioned above, the document below reflects topics the authors decided should belong in a first introduction to A 1 -homotopy theory, especially for people coming from algebraic geometry. Other surveys in the field which focus on different aspects of the theory include [Dun07], [Lev08], [Lev16], [Mor06]; a textbook reference for the ideas covered in this survey is [Mor12]. Voevodsky's ICM address pays special attention to the topological motivation for the theory in [Voe98].…”