Rigid geometry of curves and their Jacobians. ([2016])

• Record Type: Book
• Further Information: Note: Werner Lütkebohmert.
• Authors: Lütkebohmert, Werner
• Contents: Rigid Geometry of Curves and Their Jacobians; Introduction; Chapter 1: Classical Rigid Geometry; 1.1 Non-Archimedean Fields; 1.2 Restricted Power Series; 1.3 Af noid Spaces; 1.4 The Maximum Principle; 1.5 Rigid Analytic Spaces; 1.6 Coherent Sheaves; 1.7 Line Bundles; 1.8 Algebraization of Proper Rigid Analytic Curves; Chapter 2: Mumford Curves; 2.1 Tate's Elliptic Curve; 2.2 Schottky Groups; 2.3 De nition and Properties; 2.4 Skeletons; 2.5 Automorphic Functions; 2.6 Drinfeld's Polarization; 2.7 Rigid Analytic Tori and Their Duals; 2.8 Jacobian Variety of a Mumford Curve. 2.9 Riemann's Vanishing TheoremChapter 3: Formal and Rigid Geometry; 3.1 Canonical Reduction of Af noid Domains; 3.1.1 Functors AK ÅK and AKÃK; 3.1.2 Formal Analytic Spaces; 3.1.3 Finiteness Theorem of Grauert-Remmert-Gruson; 3.2 Admissible Formal Schemes; 3.3 Generic Fiber of Admissible Formal Schemes; 3.4 Reduced Fiber Theorem; 3.4.1 Analytic Method of Grauert-Remmert-Gruson; 3.4.2 Elementary Method of Epp; 3.4.3 The Natural Approach; 3.5 Complements on Flatness; 3.6 Approximation in Smooth Rigid Spaces; 3.7 Compacti cation of Smooth Curve Fibrations; Chapter 4: Rigid Analytic Curves. 4.1 Formal Fibers4.2 Genus Formula; 4.3 Meromorphic Functions; 4.4 Formal Stable Reduction; 4.5 Stable Reduction; 4.6 Universal Covering of a Curve; 4.7 Characterization of Mumford Curves; Chapter 5: Jacobian Varieties; 5.1 Jacobian of a Smooth Projective Curve; 5.2 Generalized Jacobian of a Semi-Stable Curve; 5.3 Lifting of the Jacobian of the Reduction; 5.4 Morphisms to Rigid Analytic Groups with Semi-Abelian Reduction; 5.5 Uniformization of Jacobians; 5.6 Applications to Abelian Varieties; Chapter 6: Raynaud Extensions; 6.1 Basic Facts; 6.2 Line Bundles; 6.3 Duality; 6.4 Algebraization. 6.5 Polarization of Jacobians6.6 Parameterizing Degenerating Abelian Varieties; Chapter 7: Abeloid Varieties; 7.1 Basic Facts on Abeloid Varieties; 7.2 Generation of Subgroups by Smooth Covers; 7.3 Extension of Formal Tori; 7.4 Morphisms from Curves to Groups; 7.5 Stable Reduction of Relative Curves; 7.6 The Structure Theorem; 7.7 Proof of the Structure Theorem; Appendix: Miscellaneous; A.1 Some Notions about Graphs; A.2 Torus Extensions of Formal Abelian Schemes; A.3 Cubical Structures; Glossary of Notations; References; Index.
• Publisher Details: Cham New York : Springer
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 516.3/52; Curves, Plane; Jacobians; MATHEMATICS -- Geometry -- General; Curves, Plane; Jacobians; Electronic books
• Languages: German
• ISBNs: 9783319273716; 3319273698; 9783319273693
• Related ISBNs: 331927371X; 9783319273693
• Notes: Note: Includes bibliographical references.; Note: Vendor-supplied metadata.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.