Fundamentals of Diophantine Geometry
jun 2013. · Springer Science & Business Media
E-knjiga
370
Broj stranica
reportOcjene i recenzije nisu potvrđene Saznajte više
O ovoj e-knjizi
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.
Ocijenite ovu e-knjigu
Recite nam šta mislite.
Informacije o čitanju
Pametni telefoni i tableti
Instalirajte aplikaciju Google Play Knjige za Android i iPad/iPhone uređaje. Aplikacija se automatski sinhronizira s vašim računom i omogućava vam čitanje na mreži ili van nje gdje god da se nalazite.
Laptopi i računari
Audio knjige koje su kupljene na Google Playu možete slušati pomoću web preglednika na vašem računaru.
Elektronički čitači i ostali uređaji
Da čitate na e-ink uređajima kao što su Kobo e-čitači, morat ćete preuzeti fajl i prenijeti ga na uređaj. Pratite detaljne upute Centra za pomoć da prenesete fajlove na podržane e-čitače.
