Big pictures of motivic and classical homotopy theories

Author:

Ahmad Rouintan

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Algebraic Topology (math.AT)

journal:

date:

2023-10-28 16:00:00

Abstract

Vladimir Voevodsky and Fabien Morel introduced the motivic homotopy theory in the late 90s, which is a theory meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. This theory, as proved by Oliver Rondigs and Paul Arne Ostvaer, is connected with Voevodskys triangulated category of motives. This connection is the analogue of the connection between algebraic topology and homological algebra. In this paper, we want to understand the big picture of motivic homotopy theory and its connection to motives by comparison to the classical counterpart.

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