Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Projectivity of the moduli of curves
- 2 The stack of admissible covers is algebraic
- 3 Projectivity of the moduli space of vector bundles on a curve
- 4 Boundedness of semistable sheaves
- 5 Theorem of the Base
- 6 Weil restriction for schemes and beyond
- 7 Heights over finitely generated fields
- 8 An explicit self-duality
- 9 Tannakian reconstruction of coalgebroids
7 - Heights over finitely generated fields
Published online by Cambridge University Press: 06 October 2022
Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- 1 Projectivity of the moduli of curves
- 2 The stack of admissible covers is algebraic
- 3 Projectivity of the moduli space of vector bundles on a curve
- 4 Boundedness of semistable sheaves
- 5 Theorem of the Base
- 6 Weil restriction for schemes and beyond
- 7 Heights over finitely generated fields
- 8 An explicit self-duality
- 9 Tannakian reconstruction of coalgebroids
Summary
This is an expository account about height functions and Arakelov theory in arithmetic geometry. We recall Conrad’s description of generalized global fields in order to describe heights over function fields of higher transcendence degree. We then give a brief overview of Arakelov theory and arithmetic intersection theory. Our exposition culminates in a description of Moriwaki’s Arakelov-theoretic formulation of heights, as well as a comparison of Moriwaki’s construction to various versions of heights.
Keywords
- Type
- Chapter
- Information
- Stacks Project Expository Collection , pp. 222 - 254Publisher: Cambridge University PressPrint publication year: 2022