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Number Fields and Function Fields - Two Parallel Worlds Gerard B. M. van der Geer

Number Fields and Function Fields - Two Parallel Worlds By Gerard B. M. van der Geer

Number Fields and Function Fields - Two Parallel Worlds by Gerard B. M. van der Geer

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Summary

Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas. This title contains articles which explore various aspects of the parallel worlds of function fields and number fields, ranging from Arakelov geometry to Drinfeld modules, and t-motives.

Number Fields and Function Fields - Two Parallel Worlds Summary

Number Fields and Function Fields - Two Parallel Worlds by Gerard B. M. van der Geer

Invited articles by leading researchers 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

Aimed at graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections

Number Fields and Function Fields - Two Parallel Worlds Reviews

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)

Table of Contents

* Preface * Participants * List of Contributors * G. Boeckle: Arithmetic over Function Fields: A Cohomological Approach * T. van den Bogaart and B. Edixhoven: Algebraic Stacks Whose Number of Points over Finite Fields Is a Polynomial * H. Brenner: On a Problem of Miyaoka * F. Breuer and R. Pink: Monodromy Groups Associated to Nonisotrivial Drinfeld Modules in Generic Characteristic * K. Conrad: Irreducible Values of Polynomials: A Nonanalogy * A. Deitmar: Schemes over F1 * C. Deninger and A. Werner: Line Bundles and p-Adic Characters * G. Faltings: Arithmetic Eisenstein Classes on the Siegel Space: Some Computations * U. Hartl: Uniformizing the Stacks of Abelian Sheaves * R. de Jong: Faltings' Delta-Invariant of a Hyperelliptic Riemann Surface * K. Koehler: A Hirzebruch Proportionality Principle in Arakelov Geometry * U. Kuhn: On the Height Conjecture for Algebraic Points on Curves Defined over Number Fields * J.C. Lagarias: A Note on Absolute Derivations and Zeta Functions * V. Maillot and D. Roessler: On the Order of Certain Characteristic Classes of the Hodge Bundle of Semiabelian Schemes * D. Roessler: A Note on the Manin-Mumford Conjecture

Additional information

NPB9780817643973
9780817643973
0817643974
Number Fields and Function Fields - Two Parallel Worlds by Gerard B. M. van der Geer
Gerard B. M. van der Geer
Progress in Mathematics
New
Hardback
Birkhauser Boston Inc
2005-09-14
321
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Number Fields and Function Fields - Two Parallel Worlds