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Ordered algebraic structures --- Drinfeld modules. --- Modules (Algebra) --- Quantum groups. --- Modules (Algebra).
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Algebraic geometry --- Number theory --- Algebraic fields --- Algebraic numbers --- Algebraïsche velden --- Arithmetic functions --- Corps algébriques --- Drinfeld modules --- Drinfeld modullen --- Fields [Algebraic ] --- Fonctions arithmétiques --- Modules de Drinfeld --- Rekenkundige functies --- Algebraic fields. --- Arithmetic functions. --- Drinfeld modules.
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Algebraic geometry --- Drinfeld modules. --- Deformations (Mechanics) --- Surfaces, Algebraic. --- Modules de Drinfeld --- Déformations (Mécanique) --- Surfaces algebriques --- 51 <082.1> --- Mathematics--Series --- Déformations (Mécanique) --- Drinfeld, Modules de. --- Déformations (mécanique) --- Surfaces algébriques. --- Drinfeld modules --- Surfaces, Algebraic --- Algebraic surfaces --- Geometry, Algebraic --- Modules (Algebra) --- Elastic solids --- Mechanics --- Rheology --- Strains and stresses --- Structural failures
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This textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory. After the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized. Drinfeld Modules guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.
Number theory. --- Algebra. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Number study --- Numbers, Theory of --- Algebra --- Drinfeld modules. --- Modules (Algebra) --- Mòduls de Drinfeld
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The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. It deals with: 1. The relation between conformal blocks and generalised theta functions (Lectures by S. Kumar) 2. Drinfeld Shtukas (Lectures by G. Laumon) 3. Drinfeld modules and Elliptic Sheaves (Lectures by U. Stuhler) The latter topics are useful in connection with Langlands programme for function fields. The contents of the book would give a comprehensive introduction of these topics to graduate students and researchers.
Differential geometry. Global analysis --- Vector bundles --- Drinfeld modules --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Drinfeld modullen --- Faisceaux de vecteurs --- Modules de Drinfeld --- Vecteurs [Faisceaux de ] --- Vectorenbundels --- Algebraic geometry. --- Number theory. --- Algebraic Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry --- Vector bundles. --- Drinfeld modules. --- Modules (Algebra) --- Fiber spaces (Mathematics)
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Ce livre contient une démonstration détaillée et complète de l'existence d'un isomorphisme équivariant entre les tours p-adiques de Lubin-Tate et de Drinfeld. Le résultat est établi en égales et inégales caractéristiques. Il y est également donné comme application une démonstration du fait que les cohomologies équivariantes de ces deux tours sont isomorphes, un résultat qui a des applications à l'étude de la correspondance de Langlands locale. Au cours de la preuve des rappels et des compléments sont donnés sur la structure des deux espaces de modules précédents, les groupes formels p-divisibles et la géométrie analytique rigide p-adique.
Isomorphisms (Mathematics) --- Drinfeld modules. --- Modules (Algebra) --- Categories (Mathematics) --- Group theory --- Morphisms (Mathematics) --- Set theory --- Geometry, algebraic. --- Number theory. --- Algebraic Geometry. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Algebraic geometry --- Geometry --- Algebraic geometry.
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No detailed description available for "The Arithmetic of Function Fields".
Drinfeld modules --- -Algebraic fields --- -Algebraic number fields --- -511.6 Algebraic number fields --- Algebraic fields --- 511.6 --- 511.6 Algebraic number fields --- Algebraic number fields --- Modules (Algebra) --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Congresses --- Congresses.
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This book provides an exposition of function field arithmetic withemphasis on recent developments concerning Drinfeld modules, thearithmetic of special values of transcendental functions (such as zetaand gamma functions and their interpolations), diophantineapproximation and related interesting open problems.
Algebraic fields. --- Arithmetic functions. --- Drinfeld modules. --- Modules (Algebra) --- Functions, Arithmetic --- Functions of complex variables --- Number theory --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Algebra
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Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.
Algebraic fields. --- Curves, Elliptic. --- Forms, Modular. --- Elliptic functions --- Forms, Modular --- Curves, Algebraic --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Drinfeld modules. --- Automorphic forms. --- Elliptic functions. --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Mathematics. --- Algebra. --- Category theory (Mathematics). --- Homological algebra. --- Topological groups. --- Lie groups. --- Number theory. --- Number Theory. --- Topological Groups, Lie Groups. --- Category Theory, Homological Algebra. --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Automorphic functions --- Forms (Mathematics) --- Modules (Algebra) --- Topological Groups. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Number study --- Numbers, Theory of --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Homological algebra --- Algebra, Abstract --- Homology theory --- Curves, Algebraic.
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