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AuthorAndradas, Carlos. author
TitleConstructible Sets in Real Geometry [electronic resource] / by Carlos Andradas, Ludwig Brรถcker, Jesรบs M. Ruiz
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-642-80024-5
Descript IX, 270 p. online resource

CONTENT

I. A First Look at Semialgebraic Geometry -- 1. Real Closed Fields and Transfer Principles -- 2. What is Semialgebraic Geometry? -- 3. Real Spaces -- 4. Examples -- II. Real Algebra -- 1. The Real Spectrum of a Ring -- 2. Specializations, Zero Sets and Real Ideals -- 3. Real Valuations -- 4. Real Going-Up and Real Going-Down -- 5. Abstract Semialgebraic Functions -- 6. Cylindrical Decomposition -- 7. Real Strict Localization -- Notes -- III. Spaces of Signs -- 1. The Axioms -- 2. Forms -- 3. SAP-Spaces and Fans -- 4. Local Spaces of Signs -- 5. The Space of Signs of a Ring -- 6. Subspaces -- Notes -- IV. Spaces of Orderings -- 1. The Axioms Revisited -- 2. Basic Constructions -- 3. Spaces of Finite Type -- 4. Spaces of Finite Chain Length -- 5. Finite Type = Finite Chain Length -- 6. Local-Global Principles -- 7. Representation Theorem and Invariants -- Notes -- V. The Main Results -- 1. Stability Formulae -- 2. Complexity of Constructible Sets -- 3. Separation -- 4. Real Divisors -- 5. The Artin-Lang Property -- Notes -- VI. Spaces of Signs of Rings -- 1. Fans and Valuations -- 2. Field Extensions: Upper Bounds -- 3. Field Extensions: Lower Bounds -- 4. Algebras -- 5. Algebras Finitely Generated over Fields -- 6. Archimedean Rings -- 7. Coming Back to Geometry -- Notes -- VII. Real Algebra of Excellent Rings -- 1. Regular Homomorphisms -- 2. Excellent Rings -- 3. Extension of Orderings Under Completion -- 4. Curve Selection Lemma -- 5. Dimension, Valuations and Fans -- 6. Closures of Constructible Sets -- 7. Real Going-down for Regular Homomorphisms -- 8. Connected Components of Constructible Sets -- Notes -- VIII. Real Analytic Geometry -- 1. Semianalytic Sets -- 2. Semianalytic Set Germs -- 3. Cylindrical Decomposition of Germs -- 4. Rings of Global Analytic Functions -- 5. Hilbertโ{128}{153}s 17th Problem and Real Nullstellensatz -- 6. Minimal Generation of Global Semianalytic Sets -- 7. Topology of Global Semianalytic Sets -- 8. Germs at Compact Sets -- Notes


Mathematics Algebraic geometry Mathematics Algebraic Geometry



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