| Description |
1 online resource |
| Series |
London Mathematical Society lecture note series ; 480 |
|
London Mathematical Society lecture note series ; 480.
|
| Contents |
Cover -- Half-title -- Series information -- Title page -- Copyright information -- Contents -- List of contributors -- Preface -- 1 Projectivity of the moduli of curves -- 1.1 Stable curves -- 1.2 Nakai-Moishezon criterion for ampleness -- 1.3 Positivity of invertible sheaves -- 1.4 Nef locally free sheaves -- 1.5 Ampleness lemma -- 1.6 Nefness for families of nodal curves -- 1.7 Projectivity of the moduli of curves -- 2 The stack of admissible covers is algebraic -- 2.1 Introduction -- 2.2 Setup -- 2.3 Admissible G-covers -- 3 Projectivity of the moduli space of vector bundles on a curve |
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3.1 The moduli stack of all vector bundles -- 3.2 Semistability -- 3.3 Good moduli spaces -- 3.4 Determinantal line bundles -- 3.5 Projectivity -- 4 Boundedness of semistable sheaves -- 4.1 Introduction -- 4.2 Preliminaries -- 4.3 Bogomolov's inequality -- 4.4 Restriction to hypersurfaces and Bogomolov's inequality -- 4.5 Boundedness of torsion-free sheaves -- 5 Theorem of the Base -- 5.1 The Picard functor -- 5.2 Components of the Picard functor -- 5.3 Castelnuovo-Mumford regularity -- 5.4 Boundedness -- 5.5 Finiteness of cycles modulo numerical equivalence -- 5.6 Alterations in families |
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5.7 Theorem of the Base -- 5.8 Examples of Picard schemes -- 6 Weil restriction for schemes and beyond -- 6.1 Weil restriction of schemes -- 6.2 Basic properties of Weil restriction -- 6.3 Geometric connectedness -- 6.4 Examples -- 6.5 Weil restriction of algebraic spaces -- 6.6 Olsson's theorem -- 7 Heights over finitely generated fields -- 7.1 Introduction -- 7.2 Generalized global fields -- 7.3 Heights -- 7.4 Analytic background -- 7.5 Arithmetic intersection theory and Arakelov theory -- 7.6 Moriwaki heights -- 8 An explicit self-duality -- 8.1 Introduction |
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8.2 Commutative algebra preliminaries -- 8.3 The explicit isomorphism -- 9 Tannakian reconstruction of coalgebroids -- 9.1 Introduction -- 9.2 Tannakian adjunction -- 9.3 Reconstruction -- 9.4 The embedding problem |
| Summary |
The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne-Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces |
| Subject |
Algebraic stacks.
|
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Geometry, Algebraic.
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Geometría algebraica
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Cuerpos algebraicos
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Algebraic stacks
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Geometry, Algebraic
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| Form |
Electronic book
|
| Author |
Belmans, Pieter, editor
|
|
Ho, Wei, 1983- editor.
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De Jong, Aise Johan, editor
|
| ISBN |
9781009051897 |
|
100905189X |
|
1009063286 |
|
9781009063289 |
|
