![](https://assets.cambridge.org/97810091/70321/cover/9781009170321.jpg)
- Publisher:
- Cambridge University Press
- Online publication date:
- May 2022
- Print publication year:
- 2022
- Online ISBN:
- 9781009170314
- Series:
- Cambridge Tracts in Mathematics (228)
Last updated 20/06/24: Online ordering is currently unavailable due to technical issues. We apologise for any delays responding to customers while we resolve this. For further updates please visit our website: https://www.cambridge.org/news-and-insights/technical-incident
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.
‘… a good reference for researchers intending to start work on this conjecture and related subjects.’
Ricardo Bianconi Source: MathSciNet
* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.
Usage data cannot currently be displayed.