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 ...
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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)? 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.
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Add this copy of Field Arithmetic (Ergebnisse Der Mathematik Und Ihrer to cart. $78.43, good condition, Sold by Phatpocket Limited rated 4.0 out of 5 stars, ships from Waltham Abbey, ESSEX, UNITED KINGDOM, published 1986 by Springer.
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Good. Ships from UK in 48 hours or less (usually same day). Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. 100% money back guarantee. We are a world class secondhand bookstore based in Hertfordshire, United Kingdom and specialize in high quality textbooks across an enormous variety of subjects. We aim to provide a vast range of textbooks, rare and collectible books at a great price. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. We provide a 100% money back guarantee and are dedicated to providing our customers with the highest standards of service in the bookselling industry.
Add this copy of Field Arithmetic to cart. $84.00, good condition, Sold by Munster & Company rated 5.0 out of 5 stars, ships from Corvallis, OR, UNITED STATES, published 1986 by Springer-Verlag.
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Good. Springer-Verlag, 1986. This Book is in Good Condition. Normal shelf wear to covers with very small chip to fore-edge of rear board, interior very lightly age-toned, previous owner's stamp on ffep, text is very clean with no marks, binding tight. Not Ex-Library or Remaindered. 100% Guaranteed. hardcover. Good.
Add this copy of Field Arithmetic (Ergebnisse Der Mathematik Und Ihrer to cart. $103.91, very good condition, Sold by Fireside Bookshop rated 4.0 out of 5 stars, ships from Stroud, GLOUCESTERSHIRE, UNITED KINGDOM, published 1986 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1986, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
1986
Alibris ID:
16526537591
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Very Good in No d/j as Published jacket. Size: 8vo-over 7¾"-9¾" tall; Type: Book N.B. Small plain label to inside front cover. Rubbing to corners of boards.
