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Duality theory (Mathematics) --- Fourier analysis --- Sequential analysis --- Stochastic approximation --- Analyse séquentielle --- Analyse de Fourier --- Dualité, théorie de la (Mathématiques) --- Approximation stochastique --- Data processing --- Informatique --- Analyse séquentielle --- Dualité, théorie de la (Mathématiques) --- Sequential analysis - Data processing --- Stochastic approximation - Data processing --- Duality theory (Mathematics) - Data processing --- Fourier analysis - Data processing
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Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.
Duality theory (Mathematics) --- Schemes (Algebraic geometry) --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Mathematics duality theory --- Schema's (Algebraïsche meetkunde) --- Schémas (Géometrie algébrique) --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Ordered algebraic structures --- Algebraic geometry. --- Number theory. --- Algebraic Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry --- Geometry
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This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.
Functional analysis --- Banach spaces. --- Ultraproducts. --- Duality theory (Mathematics) --- Banach spaces --- Ultraproducts --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Banach [Espaces de ] --- Banach [Ruimten van ] --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Mathematics duality theory --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Functional analysis. --- Topology. --- Geometry. --- Functional Analysis. --- Euclid's Elements --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations
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Stochastic processes --- Sequential analysis --- Optimal stopping (Mathematical statistics) --- Dualité, théorie de la (Mathématiques) --- 519.216 --- Mathematical statistics --- Statistical decision --- Stopping, Optimal (Mathematical statistics) --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Sequential analysis. --- Optimal stopping (Mathematical statistics). --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Arrêt optimal (Statistique mathématique) --- Dualité, théorie de la (Mathématiques) --- Arrêt optimal (Statistique mathématique)
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Confidence intervals --- Sequential analysis --- Statistical hypothesis testing --- Intervalles de confiance --- Dualité, théorie de la (Mathématiques) --- Tests d'hypothèses (Statistique) --- 519.244 --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Distribution (Probability theory) --- Hypothesis --- Mathematical statistics --- Statistical decision --- Confidence limits --- Confidence regions --- Intervals, Confidence --- Limits, Confidence --- Regions, Confidence --- Sampling (Statistics) --- Statistical tolerance regions --- Sequential methods. Optimal stopping. Cusum technique (cumulative sum technique) --- Confidence intervals. --- Sequential analysis. --- Statistical hypothesis testing. --- 519.244 Sequential methods. Optimal stopping. Cusum technique (cumulative sum technique) --- Dualité, théorie de la (Mathématiques) --- Tests d'hypothèses (Statistique)
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