Description
Book SynopsisProvides an account of the triangulated theory of motives. The book’s purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology, and Chow groups.
Table of Contents* Etale motivic theory: * Etale sheaves with transfers * The relative Picard group and Suslin's rigidity theorem * Derived tensor products $\mathbb{A}^1$-weak equivalence * Etale motivic cohomology and algebraic singular homology * Nisnevich sheaves with transfers: * Standard triples * Nisnevich sheaves* * Nisnevich sheaves with transfers * The triangulated category of motives: * The category of motives * The complex $\mathbb{Z}(n)$ and $\mathbb{P}^n$ Equidimensional cycles * Higher Chow groups: * Higher Chow groups * Higher Chow groups and equidimensional cycles * Motivic cohomology and higher Chow groups * Geometric motives * Zariski sheaves with transfers: Covering morphisms of triples * Zariski sheaves with transfers * Contractions * Homotopy invariance of cohomology * Bibliography * Glossary * Index
