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
5 - Theorem of the Base
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
We explain a proof of the Theorem of the Base: the Neron– Severi group of a proper variety is a finitely generated abelian group. We discuss, quite generally, the Picard functor and its torsion and identity components. We study representability and finiteness properties of the Picard functor, both absolutely and in families. Along the way, we streamline the original proof by using alterations, and we discuss some examples of peculiar Picard schemes.
- Type
- Chapter
- Information
- Stacks Project Expository Collection , pp. 163 - 193Publisher: Cambridge University PressPrint publication year: 2022
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