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Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11) - Fried, Michael D. D.
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Fried, Michael D. D.:

Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11) - Paperback

2010, ISBN: 9783642095948

Mitwirkende: Jarden, Moshe, Springer, Taschenbuch, Auflage: Softcover reprint of hardcover 3rd ed. 2008, 816 Seiten, Publiziert: 2010-10-19T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.:… More...

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Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11) - Fried, Michael D. D.
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Fried, Michael D. D.:

Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11) - Paperback

2010, ISBN: 9783642095948

Mitwirkende: Jarden, Moshe, Springer, Taschenbuch, Auflage: Softcover reprint of hardcover 3rd ed. 2008, 816 Seiten, Publiziert: 2010-10-19T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.:… More...

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Field Arithmetic: 11 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11) - Fried, Michael D. Jarden, Moshe
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Fried, Michael D. Jarden, Moshe:
Field Arithmetic: 11 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11) - Paperback

2010

ISBN: 9783642095948

Springer, Paperback, Auflage: Softcover reprint of hardcover 3rd ed. 2008, 816 Seiten, Publiziert: 2010-10-19T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: biography, 1.13 kg, Operation… More...

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Michael D. Fried,Moshe Jarden:
Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 11) - Paperback

2010, ISBN: 9783642095948

Springer, October 2010. Trade . Good. Good Softcover. This edition reprinted in China by World Publishing in apparently 1989. Light to moderate soiling and shelfwear to covers. Tearing … More...

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Michael D. Fried:
Field Arithmetic (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a Series of Modern Surveys in Mathemati) - Paperback

2008, ISBN: 3642095941

[EAN: 9783642095948], Neubuch, [PU: Springer], 3rd edition. 816 pages. 9.10x6.10x1.70 inches. In Stock., Books

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Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11)
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ISBN:

9783642095948


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)?The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005.

Details of the book - Field Arithmetic (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 11)


EAN (ISBN-13): 9783642095948
ISBN (ISBN-10): 3642095941
Hardcover
Paperback
Publishing year: 2010
Publisher: Springer
816 Pages
Weight: 1,210 kg
Language: eng/Englisch

Book in our database since 2011-04-16T21:00:45+01:00 (London)
Detail page last modified on 2023-11-07T17:43:54+00:00 (London)
ISBN/EAN: 9783642095948

ISBN - alternate spelling:
3-642-09594-1, 978-3-642-09594-8
Alternate spelling and related search-keywords:
Book author: michael fried, jarden, shafarevich
Book title: field arithmetic, surveys modern mathematics, mathematik

Information from Publisher

Author: Michael D. Fried
Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics; Field Arithmetic
Publisher: Springer; Springer Berlin
792 Pages
Publishing year: 2010-10-19
Berlin; Heidelberg; DE
Printed / Made in
Weight: 1,229 kg
Language: English
186,99 € (DE)

BC; Algebra; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Algebra; Verstehen; Absolute Galois Groups; Algebra; Arithmetic; Counting; Finite Fields; Galois Stratification; Hilbertian Fields; Morphism; PAC Fields; Profinite Groups; Variable; geometry; number theory; theorem; Mathematics, general; Algebraic Geometry; Field Theory and Polynomials; Geometry; Mathematical Logic and Foundations; Algebra; Mathematics; Algebraic Geometry; Field Theory and Polynomials; Geometry; Mathematical Logic and Foundations; Mathematik; Algebraische Geometrie; Geometrie; Mathematik: Logik; Mathematische Grundlagen; BB

Infinite Galois Theory and Profinite Groups. - Valuations and Linear Disjointness. - Algebraic Function Fields of One Variable. - The Riemann Hypothesis for Function Fields. - Plane Curves. - The Chebotarev Density Theorem. - Ultraproducts. - Decision Procedures. - Algebraically Closed Fields. - Elements of Algebraic Geometry. - Pseudo Algebraically Closed Fields. - Hilbertian Fields. - The Classical Hilbertian Fields. - Nonstandard Structures. - Nonstandard Approach to Hilbert's Irreducibility Theorem. - Galois Groups over Hilbertian Fields. - Free Profinite Groups. - The Haar Measure. - Effective Field Theory and Algebraic Geometry. - The Elementary Theory of e-Free PAC Fields. - Problems of Arithmetical Geometry. - Projective Groups and Frattini Covers. - PAC Fields and Projective Absolute Galois Groups. - Frobenius Fields. - Free Profinite Groups of Infinite Rank. - Random Elements in Free Profinite Groups. - Omega-Free PAC Fields. - Undecidability. - Algebraically Closed Fields with Distinguished Automorphisms. - Galois Stratification. - Galois Stratification over Finite Fields. - Problems of Finite Arithmetic.
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