Field Arithmetic: Edition 2
ago 2005 · Springer Science & Business Media
eBook
780
Páginas
reportLas valoraciones y las reseñas no se verifican. Más información
Información sobre este eBook
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Valorar este eBook
Danos tu opinión.
Información sobre cómo leer
Smartphones y tablets
Instala la aplicación Google Play Libros para Android y iPad/iPhone. Se sincroniza automáticamente con tu cuenta y te permite leer contenido online o sin conexión estés donde estés.
Ordenadores portátiles y de escritorio
Puedes usar el navegador web del ordenador para escuchar audiolibros que hayas comprado en Google Play.
eReaders y otros dispositivos
Para leer en dispositivos de tinta electrónica, como los lectores de libros electrónicos de Kobo, es necesario descargar un archivo y transferirlo al dispositivo. Sigue las instrucciones detalladas del Centro de Ayuda para transferir archivos a lectores de libros electrónicos compatibles.
