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Field Arithmetic

Name: Field Arithmetic
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 05275229
Price: 73986 HUF
Availability: InStock
Author: Michael D. Fried
ISBN: 9783540772699

Michael D. Fried

Moshe Jarden

Language

English

Book Hardback

Libristo code: 05275229

Publishers Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, May 2008

Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self... Full description

Libristo code: 05275229

504 b

73 986 Ft

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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)?