000			04508nam a22006015i 4500
003			DE-He213
005			20191011094547.0
007			cr nn 008mamaa
008			100301s2005 gw | s |||| 0|eng d
020	6	4	_a9783540269496 _9978-3-540-26949-6
024	8	7	_a10.1007/b138352 _2doi
050	8	4	_a Libro electrónico
072	8	7	_aPBF _2bicssc
072	8	7	_aMAT002000 _2bisacsh
082			_a512 _223
100	8	1	_aFried, Michael D. _eauthor. _9101190
245	9	7	_aField Arithmetic _h[electronic resource] / _cby Michael D. Fried, Moshe Jarden.
001			000064651
246	8	3	_aRevised and Enlarged by Moshe Jarden
250	6	4	_aSecond Edition.
300	6	4	_aXXIII, 780 p. _bonline resource.
490	8	1	_aA Series of Modern Surveys in Mathematics ; _v11
505	8	0	_aInfinite 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 Hilberts 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 Profinite Groups -- Omega-free PAC Fields -- Undecidability -- Algebraically Closed Fields with Distinguished Automorphisms -- Galois Stratification -- Galois Stratification over Finite Fields -- Problems of Field Arithmetic.
520	6	4	_aField 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)?
650	8	0	_aMathematics. _98571
650	8	0	_aAlgebra. _9160
650	8	0	_aGeometry, algebraic. _9101191
650	8	0	_aField theory (Physics). _912461
650	8	0	_aGeometry. _99802
650	8	0	_aLogic, Symbolic and mathematical. _914063
650	8	0	_aNumber theory. _9101192
650			_aMathematics. _98571
650			_aAlgebra. _9160
650			_aAlgebraic Geometry. _9101193
650			_aField Theory and Polynomials. _912463
650			_aGeometry. _99802
650			_aMathematical Logic and Foundations. _914067
650			_aNumber Theory. _9101194
700	8	1	_aJarden, Moshe. _eauthor. _9101195
710	8	2	_aSpringerLink (Online service) _9101196
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783540228110
830	8	0	_aA Series of Modern Surveys in Mathematics ; _v11 _9101197
856			_uhttp://dx.doi.org/10.1007/b138352 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2005.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
999			_c59291 _d59291
942			_c05