Field Arithmetic

Name: Field Arithmetic
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783540772699
Price: 201.92 EUR
Availability: InStock

Автор: Michael D. Fried, Moshe Jarden

Език:

Корици: С твърди корици

Издател: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Наличност: Външен склад

Изпращаме след 10-18 дни

201.92 € 394.92 лв

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

Информация за книгата

Автор

Michael D. Fried, Moshe Jarden

Език

Английски език

Корици

Книга - С твърди корици

Издадена

2008

страници

792

EAN

9783540772699

ISBN

3540772693

Enbook ID

05275229

Издател

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Теглоt

1302

Размери

160 x 240 x 49

Пълно описание

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)?

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Field Arithmetic

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