conjectures arithmetic algebraic geometry von hulsbergen wilfred (31 Ergebnisse)

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.

Taschenbuch. Zustand: Neu. Conjectures in Arithmetic Algebraic Geometry | A Survey | Wilfred W. J. Hulsbergen | Taschenbuch | vii | Englisch | 1992 | Vieweg & Teubner | EAN 9783528064334 | Verantwortliche Person für die EU: Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Str. 46, 65189 Wiesbaden, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

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Taschenbuch. Zustand: Neu. Conjectures in Arithmetic Algebraic Geometry | A Survey | Wilfred W. J. Hulsbergen | Taschenbuch | vii | Englisch | 2013 | Vieweg & Teubner | EAN 9783663095071 | Verantwortliche Person für die EU: Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Str. 46, 65189 Wiesbaden, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math ematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce L functions, the main, motivation being the calculation of class numbers. In partic ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geome try only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind.

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Gebundene Ausgabe. 236 Seiten 1992. Einband leicht berieben, sonst sehr gut. Sprache: Deutsch.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory. 240 pp. Deutsch.

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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 1 The zero-dimensional case: number fields.- 1.1 Class Numbers.- 1.2 Dirichlet L-Functions.- 1.3 The Class Number Formula.- 1.4 Abelian Number Fields.- 1.5 Non-abelian Number Fields and Artin L-Functions.- 2 The one-dimensional case: elliptic curves.- 2.1 G.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math ematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce L functions, the main, motivation being the calculation of class numbers. In partic ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properties of L-functions. Twentieth century number theory, class field theory and algebraic geome try only strengthen the nineteenth century number theorists's view. We just mention the work of E. H~cke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind. 246 pp. Englisch.

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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Dr. Wilfried Hulsbergen is teaching at the KMA, Breda,Niederlande.In the early 1980 s, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fiel.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -1 The zero-dimensional case: number fields.- 1.1 Class Numbers.- 1.2 Dirichlet L-Functions.- 1.3 The Class Number Formula.- 1.4 Abelian Number Fields.- 1.5 Non-abelian Number Fields and Artin L-Functions.- 2 The one-dimensional case: elliptic curves.- 2.1 General Features of Elliptic Curves.- 2.2 Varieties over Finite Fields.- 2.3 L-Functions of Elliptic Curves.- 2.4 Complex Multiplication and Modular Elliptic Curves.- 2.5 Arithmetic of Elliptic Curves.- 2.6 The Tate-Shafarevich Group.- 2.7 Curves of Higher Genus.- 2.8 Appendix.- 3 The general formalism of L-functions, Deligne cohomology and Poincaré duality theories.- 3.1 The Standard Conjectures.- 3.2 Deligne-Beilinson Cohomology.- 3.3 Deligne Homology.- 3.4 Poincaré Duality Theories.- 4 Riemann-Roch, K-theory and motivic cohomology.- 4.1 Grothendieck-Riemann-Roch.- 4.2 Adams Operations.- 4.3 Riemann-Roch for Singular Varieties.- 4.4 Higher Algebraic K-Theory.- 4.5 Adams Operations in Higher Algebraic K-Theory.- 4.6 Chern Classes in Higher Algebraic K-Theory.- 4.7 Gillet's Riemann-Roch Theorem.- 4.8 Motivic Cohomology.- 5 Regulators, Deligne's conjecture and Beilinson's first conjecture.- 5.1 Borel's Regulator.- 5.2 Beilinson's Regulator.- 5.3 Special Cases and Zagier's Conjecture.- 5.4 Riemann Surfaces.- 5.5 Models over Spec(Z).- 5.6 Deligne's Conjecture.- 5.7 Beilinson's First Conjecture.- 6 Beilinson's second conjecture.- 6.1 Beilinson's Second Conjecture.- 6.2 Hilbert Modular Surfaces.- 7 Arithmetic intersections and Beilinson's third conjecture.- 7.1 The Intersection Pairing.- 7.2 Beilinson's Third Conjecture.- 8 Absolute Hodge cohomology, Hodge and Tate conjectures and Abel-Jacobi maps.- 8.1 The Hodge Conjecture.- 8.2 Absolute Hodge Cohomology.- 8.3 Geometric Interpretation.- 8.4Abel-Jacobi Maps.- 8.5 The Tate Conjecture.- 8.6 Absolute Hodge Cycles.- 8.7 Motives.- 8.8 Grothendieck's Conjectures.- 8.9 Motives and Cohomology.- 9 Mixed realizations, mixed motives and Hodge and Tate conjectures for singular varieties.- 9.1 Tate Modules.- 9.2 Mixed Realizations.- 9.3 Weights.- 9.4 Hodge and Tate Conjectures.- 9.5 The Homological Regulator.- 10 Examples and Results.- 10.1 B & S-D revisited.- 10.2 Deligne's Conjecture.- 10.3 Artin and Dirichlet Motives.- 10.4 Modular Curves.- 10.5 Other Modular Examples.- 10.6 Linear Varieties.Vieweg+Teubner Verlag, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 252 pp. Englisch.

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