Fundamentals of Diophantine Geometry - Image 1

£61.43

Springer Fundamentals of Diophantine Geometry

Name: Fundamentals of Diophantine Geometry
Brand: Springer
Price: 61.43 GBP
Availability: InStock

Geometry & Topology

Price History & Forecast

Last 29 days • 29 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 29 days • 1 price levels

Days at Price

Price Analysis

Most common price: £61 (29 days, 100.0%)

Price range: £61 - £61

Price levels: 1 different prices over 29 days

Description

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 1441928189
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Geometry & Topology
Domain: Amazon UK
Release Date: 03 December 2010
Listed Since: 06 July 2010

Barcode

No barcode data available

Springer Fundamentals of Diophantine Geometry

Price History & Forecast

Price Distribution

Price Analysis

Description

Product Specifications

Barcode

Similar Products You Might Like

Fundamentals of Diophantine Geometry

Number Theory III: Diophantine Geometry

Basic Algebraic Geometry (Springer Study Edition)

Birational Geometry, Rational Curves, and Arithmetic

Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)

Algebraic Surfaces In Positive Characteristics: Purely Inseparable Phenomena In Curves And Surfaces

Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics): 20

Ideals and Reality: Projective Modules and Number of Generators of Ideals (Springer Monographs in Mathematics)

Number Theory: Algebraic Numbers and Functions (Graduate Studies in Mathematics)

Number Theory and Geometry: An Introduction to Arithmetic Geometry (Pure and Applied Undergraduate Texts)

Algebraic Geometry: An Introduction (Universitext)

Affine Algebraic Geometry: Geometry Of Polynomial Rings: 11 (Series on University Mathematics)

Arithmetic Fundamental Groups and Noncommutative Algebra Book

Effective Methods in Algebraic Geometry: 94 (Progress in Mathematics)

Introduction to Elliptic Curves and Modular Forms: 97 (Graduate Texts in Mathematics, 97)

Number Theory in Function Fields: 210 (Graduate Texts in Mathematics, 210)

Number Theory: Volume II: Analytic and Modern Tools: 240 (Graduate Texts in Mathematics, 240)

Algebraic Geometry II: Cohomology of Schemes: With Examples and Exercises (Springer Studium Mathematik - Master)

Arithmetic of Quadratic Forms (Springer Monographs in Mathematics)

Diophantine Analysis

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation: 350 (Grundlehren der mathematischen Wissenschaften, 350)

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation: 350 (Grundlehren der mathematischen Wissenschaften, 350)

Field Arithmetic: 11 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11)

Geometry of Algebraic Curves: Volume I: 267 (Grundlehren der mathematischen Wissenschaften, 267)