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. 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. Weonce 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. Third revised editionof the classic Ergebnisse volume ‘Field Arithmetic’ by M. Fried and M. JardenImproves the second edition in two ways: Removes many typos and mathematical inaccuracies that appeared in the second edition (in particular fills a gap inthe references) Reports on five open problems of the second edition that weresolved since that edition appeared in 2005
- ISBN: 978-3-540-77269-9
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 792
- Fecha Publicación: 01/05/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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- ÁLGEBRA