April 4, 2024Open Access

An introduction to mixed Tate motives

Key Points

Mixed Tate motives are central to understanding cohomology groups and their arithmetic invariants in algebraic varieties.
Key topics include connections to multiple zeta values and polylogarithms, impacting algebraic K-theory and more.
Analysis focuses on various facets of mixed Tate motives, promoting further exploration in algebra and geometry fields in June 2022 at a summer school in Strasbourg, France, with attendees including mathematicians and students in the field where they are being used.

Abstract

Mixed Tate motives are central objects in the study of cohomology groups of algebraic varieties and their arithmetic invariants. They also play a crucial role in a wide variety of questions related to multiple zeta values and polylogarithms, algebraic K-theory, hyperbolic geometry, and particle physics among others. This survey article is an introduction to mixed Tate motives and their many facets. It was written for the proceedings of the Summer School on Motives and Arithmetic Groups held in Strasbourg in June 2022.

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