Number Fields and Function Fields—Two Parallel Worlds

• Corporate Author: SpringerLink (Online service)
• Other Authors: Geer, Gerard van der (Editor), Moonen, Ben (Editor), Schoof, René (Editor)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2005.
• Series: Progress in Mathematics ; 239
• Subjects: Mathematics.; Algebraic geometry.; Number theory.; Physics.; Algebraic Geometry.; Number Theory.; Mathematical Methods in Physics.

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...

Table of Contents:

• 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.