Point-Counting and the Zilber-Pink Conjecture (Hardcover) (ISBN-13: 9781009170321)

Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André-Oort and Zilber-Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.

Author: Jonathan Pila
ISBN-10: 1009170325
ISBN-13: 9781009170321
Publisher: Cambridge University Press
Language: English
Published: 06/09/2022
Pages: 268
Format: Hardcover
Weight: 1.24lbs
Size: 9.00h x 6.00w x 0.75d