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" Number fields and function fields : "
Gerard van der Geer, Ben Moonen, René Schoof, editors.
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BL
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| Record Number
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976601
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b730971
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| Title & Author
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Number fields and function fields : : two parallel worlds /\ Gerard van der Geer, Ben Moonen, René Schoof, editors.
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| Publication Statement
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Boston :: Birkhäuser,, ©2005.
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| Series Statement
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Progress in mathematics ;; v. 239
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1 online resource (xiii, 318 pages)
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| ISBN
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0817643974
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: 0817644474
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: 6610724652
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: 9780817643973
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: 9780817644475
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: 9786610724659
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Arithmetic over function fields : a cohomological approach / Gebhard Böckle -- Algebraic stacks whose number of points over finite fields is a polynomial / Theo van den Bogaart and Bas Edixhoven -- On a problem of Miyaoka / Holger Brenner -- Monodromy groups associated to non-isotrivial drinfeld modules in generic characteristic / Florian Breuer and Richard Pink -- Irreducible values of polynomials : a non-analogy / Keith Conrad -- Schemes over F1 / Anton Deitmar -- Line bundles and p-adic characters / Christopher Deninger and Annette Werner -- Arithmetic Eisenstein classes on the Siegel space : some computations / Gerd Faltings -- Uniformizing the stacks of Abelian sheaves / Urs Hartl -- Faltings' delta-invariant of a hyperelliptic Riemann suface / Robin de Jong -- A Hirzebruch proportionality principle in Arakelov geometry / Kai Köhler -- On the height conjecture for algebraic points on curves defined over number fields / Ulf Kühn -- A note on absolute derivations and zeta functions / Jeffrey C. Lagaris -- On the order of certain characteristic classes of the Hodge Bundle of semi-abelian schemes / Vincent Maillot and Damian Roessler -- A note on the Manin-Mumford conjecture / Damian Roessler.
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| Abstract
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Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. The arrival of Arakelov's new geometry that tries to put the archimedean places on a par with the finite ones gave a new impetus and led to spectacular success in Faltings' hands. There are numerous further examples where ideas or techniques from the more geometrically-oriented world of function fields have led to new insights in the more arithmetically-oriented world of number fields, or vice versa. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections. Contributors: G. Böckle; T. van den Bogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R. de Jong; K. Köhler; U. Kühn; J.C. Lagarias; V. Maillot; R. Pink; D. Roessler; and A. Werner.
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| Subject
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Algebraic fields.
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Finite fields (Algebra)
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Corps algébriques.
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Corps finis.
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Algebraic fields.
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Finite fields (Algebra)
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MATHEMATICS-- Algebra-- Intermediate.
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Algebraïsche getallen.
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Diofantische vergelijkingen.
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| Dewey Classification
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512/.3
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| LC Classification
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QA247.N86 2005eb
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| NLM classification
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31.14bcl
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31.51bcl
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| Added Entry
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Geer, Gerard van der.
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Moonen, Ben.
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Schoof, René.
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