Periods and Nori Motives - Volume 65

This text 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 approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties.

Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics.

There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives.