Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Glossary of Frequently Used Notation
- History and Summary
- 1 Ineffective Results for Diophantine Equations over Finitely Generated Domains
- 2 Effective Results for Diophantine Equations over Finitely Generated Domains: The Statements
- 3 A Brief Explanation of Our Effective Methods over Finitely Generated Domains
- 4 Effective Results over Number Fields
- 5 Effective Results over Function Fields
- 6 Tools from Effective Commutative Algebra
- 7 The Effective Specialization Method
- 8 Degree-Height Estimates
- 9 Proofs of the Results from Sections 2.2 to 2.5 Use of Specializations
- 10 Proofs of the Results from Sections 2.6 to 2.8 Reduction to Unit Equations
- References
- Index
7 - The Effective Specialization Method
Published online by Cambridge University Press: 31 August 2022
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Glossary of Frequently Used Notation
- History and Summary
- 1 Ineffective Results for Diophantine Equations over Finitely Generated Domains
- 2 Effective Results for Diophantine Equations over Finitely Generated Domains: The Statements
- 3 A Brief Explanation of Our Effective Methods over Finitely Generated Domains
- 4 Effective Results over Number Fields
- 5 Effective Results over Function Fields
- 6 Tools from Effective Commutative Algebra
- 7 The Effective Specialization Method
- 8 Degree-Height Estimates
- 9 Proofs of the Results from Sections 2.2 to 2.5 Use of Specializations
- 10 Proofs of the Results from Sections 2.6 to 2.8 Reduction to Unit Equations
- References
- Index
Summary
We describe in full detail our effective specialization method, which allows us to reduce effective finiteness results for Diophantine equations over finitely generated domains to effective results over number fields and function fields, discussed in Chapters 4 and 5.
- Type
- Chapter
- Information
- Effective Results and Methods for Diophantine Equations over Finitely Generated Domains , pp. 128 - 155Publisher: Cambridge University PressPrint publication year: 2022