Cyclotomic Fields II
12/2012 · Graduate Texts in Mathematics Livro 69 · Springer Science & Business Media
Livro eletrónico
164
Páginas
reportAs classificações e as críticas não são validadas Saiba mais
Acerca deste livro eletrónico
This second volume incorporates a number of results which were discovered and/or systematized since the first volume was being written. Again, I limit myself to the cyclotomic fields proper without introducing modular func tions. As in the first volume, the main concern is with class number formulas, Gauss sums, and the like. We begin with the Ferrero-Washington theorems, proving Iwasawa's conjecture that the p-primary part of the ideal class group in the cyclotomic Zp-extension of a cyclotomic field grows linearly rather than exponentially. This is first done for the minus part (the minus referring, as usual, to the eigenspace for complex conjugation), and then it follows for the plus part because of results bounding the plus part in terms of the minus part. Kummer had already proved such results (e.g. if p, (h; then p, (h;). These are now formulated in ways applicable to the Iwasawa invariants, following Iwasawa himself. After that we do what amounts to " Dwork theory," to derive the Gross Koblitz formula expressing Gauss sums in terms of the p-adic gamma function. This lifts Stickel berger's theorem p-adically. Half of the proof relies on a course of Katz, who had first obtained Gauss sums as limits of certain factorials, and thought of using Washnitzer-Monsky cohomology to prove the Gross-Koblitz formula
Classifique este livro eletrónico
Dê-nos a sua opinião.
Informações de leitura
Smartphones e tablets
Instale a app Google Play Livros para Android e iPad/iPhone. A aplicação é sincronizada automaticamente com a sua conta e permite-lhe ler online ou offline, onde quer que esteja.
Portáteis e computadores
Pode ouvir audiolivros comprados no Google Play através do navegador de Internet do seu computador.
eReaders e outros dispositivos
Para ler em dispositivos e-ink, como e-readers Kobo, tem de transferir um ficheiro e movê-lo para o seu dispositivo. Siga as instruções detalhadas do Centro de Ajuda para transferir os ficheiros para os e-readers suportados.
