Number Fields and Function Fields – Two Parallel Worlds

Inbunden, Engelska, 2005

AvGerard B. M. van der Geer,BJJ Moonen,René Schoof

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Ever since the analogy between number fields and function fields was discovered in the 19th century it has been and remains a source of inspiration for new ideas. A deeper understanding of this correlation could have tremendous consequences for the search for a unified approach that has become a sort of Holy Grail. 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 include: G. Boeckle; T. van den Boogaart; H. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; G. Harder; U. Hartl; R. de Jong; K. Koehler; U. Kuehn; J. Lagarias; T. Oda; R. Pink; D. Roessler; U. Stuhler; and A. Werner.

Produktinformation

Utgivningsdatum2005-09-14
Mått155 x 235 x 24 mm
Vikt670 g
FormatInbunden
SpråkEngelska
SerieProgress in Mathematics
Antal sidor321
Upplaga2005
FörlagBirkhauser Boston Inc
ISBN9780817643973

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik

Arithmetic over Function Fields: A Cohomological Approach.- Algebraic Stacks Whose Number of Points over Finite Fields is a Polynomial.- On a Problem of Miyaoka.- Monodromy Groups Associated to Non-Isotrivial Drinfeld Modules in Generic Characteristic.- Irreducible Values of Polynomials: A Non-Analogy.- Schemes over .- Line Bundles and p-Adic Characters.- Arithmetic Eisenstein Classes on the Siegel Space: Some Computations.- Uniformizing the Stacks of Abelian Sheaves.- Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface.- A Hirzebruch Proportionality Principle in Arakelov Geometry.- On the Height Conjecture for Algebraic Points on Curves Defined over Number Fields.- A Note on Absolute Derivations and Zeta Functions.- On the Order of Certain Characteristic Classes of the Hodge Bundle of Semi-Abelian Schemes.- A Note on the Manin-Mumford Conjecture.

From the reviews: "I thoroughly enjoyed the book; referring to it now and then through the various pages has been a wonderful experience. ... It is a stimulating and well-researched volume, aimed at a wide audience of gradute students, mathematicians, and researchers interested in geometry and arithmetic and their connections. In short, it places a most engaging progress in mathematics volume in the hands of the target audience who will enjoy, not just profit from, the different aspects of the involved parallelism." (Current Engineering Practice, Vol. 48, 2005-2006)