G. Geer: Arithmetic Algebraic Geometry

Cover: 9781461267690 | Arithmetic Algebraic Geometry | G. Geer (u. a.) | Taschenbuch | x

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Beschreibung

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Zusammenfassung

Inhaltsverzeichnis

Well-Adjusted Models for Curves over Dedekind Rings.- On the Manin Constants of Modular Elliptic Curves.- The Action of Monodromy on Torsion Points of Jacobians.- An Exceptional Isomorphism between Modular Varieties.- Chern Functors.- Curves of Genus 2 Covering Elliptic Curves and an Arithmetical Application.- Jacobians with Complex Multiplication.- Familles de Courbes Hyperelliptiques à Multiplications Réelles.- Séries de Kronecker et Fonctions L des Puissances Symétriques de Courbes Elliptiques sur Q.- Hyperelliptic Supersingular Curves.- Letter to Don Zagier.- The Old Subvariety of J0(pq).- Kolyvagin's System of Gauss Sums.- The Exponents of the Groups of Points on the Reductions of an Elliptic Curve.- The Generalized De Rham-Witt Complex and Congruence Differential Equations.- Arithmetic Discriminants and Quadratic Points on Curves.- The Birch-Swinnerton-Dyer Conjecture from a Naive Point of View.- Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields.- Finiteness Theorems for Dimensions of Irreducible ?-adic Representations.

Details

Erscheinungsjahr:	2012
Fachbereich:	Arithmetik & Algebra
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Progress in Mathematics
Inhalt:	x 444 S.
ISBN-13:	9781461267690
ISBN-10:	1461267692
Sprache:	Englisch
Herstellernummer:	80102104
Einband:	Kartoniert / Broschiert
Autor:	Geer, Gerard B. M. van der Oort, F. Steenbrink, Joseph H. M.
Redaktion:	Geer, G. Oort, F. Steenbrink, J. H. M.
Herausgeber:	G van der Geer/F Oort/J H M Steenbrink
Hersteller:	Birkhäuser Birkhäuser Boston Progress in Mathematics
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	279 x 210 x 25 mm
Von/Mit:	G. Geer (u. a.)
Erscheinungsdatum:	11.10.2012
Gewicht:	1,112 kg