The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives

This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s a

This book contains selected chapters on perfectoid spaces, their introduction and applications, as invented by Peter Scholze in his Fields Medal winning work. T