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Author Fried, Michael D
Title Field Arithmetic [electronic resource] / by Michael D. Fried, Moshe Jarden
Imprint Berlin, Heidelberg : Springer Berlin Heidelberg, 1986
book jacket
Descript 1 online resource (xvii, 460 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics, 0071-1136 ; 11
Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics ; 11
Note 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)?
Link Print version: 9783662072189
Subject Mathematics
Geometry, Algebraic
Field theory (Physics)
Logic, Symbolic and mathematical
Field theory (Physics) fast (OCoLC)fst00923918
Geometry, Algebraic. fast (OCoLC)fst00940902
Logic, Symbolic and mathematical. fast (OCoLC)fst01002068
Mathematics. fast (OCoLC)fst01012163
Electronic books
Alt Author Jarden, Moshe
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