<p>This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of &#960;, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.</p>

Transcendence and Linear Relations of 1-Periods (Cambridge Tracts in Mathematics)

Science & Math

Wüstholz, Gisbert

Huber, Annette

Mathematics

Cambridge University Press

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 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. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting.Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.

Periods and Nori Motives (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 65)

Müller-Stach, Stefan

Springer

See the best price to sell, buy, or rent books by Huber, Annette. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Huber, Annette