Point-Counting and the Zilber-Pink Conjecture

Point-counting results for sets in real Euclidean space have found applications to diophantine geometry, enabling progress on the André–Oort and Zilber–Pink conjectures. This book describes the counting results and their applications, along with their model-theoretic and transcendence connections, and serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.

Format: Hardback
Length: 268 pages
Publication date: 09 June 2022
Publisher: Cambridge University Press

Point-counting results for sets in real Euclidean space have proven to be highly valuable in the field of diophantine geometry, leading to significant advancements in the André–Oort and Zilber–Pink conjectures. These results combine concepts from transcendence theory with the robust tameness properties of sets that can be defined within an o-minimal structure, thus bridging the gap between model theory, transcendence theory, and arithmetic. This comprehensive book delves into the counting results and their diverse applications, while also exploring their model-theoretic and transcendence connections. Key results are presented in depth to showcase the versatility of the method, while broader developments are presented to illustrate the scope of the diophantine conjectures and to highlight essential arithmetical ingredients. The underlying ideas are fundamental, and most of the book can be understood with a basic familiarity in number theory and complex algebraic geometry. It serves as an invaluable introduction for postgraduate students and researchers seeking to delve into the latest developments, results, problems, and themes in this dynamic field of research.

Weight: 546g
Dimension: 158 x 235 x 28 (mm)
ISBN-13: 9781009170321