An edition of Field Arithmetic (2005)

Field Arithmetic

Field Arithmetic
Michael D. D. Fried, Moshe Jar ...
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Last edited by MARC Bot
September 28, 2024 | History
An edition of Field Arithmetic (2005)

Field Arithmetic

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)?

Publish Date
Publisher
Springer
Language
English
Pages
460

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Edition Availability
Cover of: Field Arithmetic
Field Arithmetic
2024, Springer
in English
Cover of: Field Arithmetic
Field Arithmetic
2023, Springer
in English
Cover of: Field Arithmetic
Field Arithmetic
2013, Springer
in English
Cover of: Field Arithmetic
Field Arithmetic
Dec 08, 2010, Springer
paperback
Cover of: Field Arithmetic
Field Arithmetic
2007, Springer London, Limited
in English
Cover of: Field Arithmetic
Field Arithmetic
May 05, 2005, Springer
paperback

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Book Details


Classifications

Library of Congress
QA247-247.45, QA161.A-161.Z, QA161.P59

The Physical Object

Pagination
xvii, 460
Number of pages
460

ID Numbers

Open Library
OL37425490M
ISBN 13
9783662072165

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
September 28, 2024 Edited by MARC Bot import existing book
March 1, 2022 Created by ImportBot Imported from Better World Books record