Field Arithmetic
Publication year: 2008
ISBN: 978-3-540-77270-5
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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.
Subject: Mathematics and Statistics, Absolute Galois Groups, Algebra, Arithmetic, Counting, Finite Fields, Galois Stratification, Hilbertian Fields, Morphism, PAC Fields, Profinite Groups, Variable, geometry, number theory, theorem
