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Fried M.D., Jarden M. — Field Arithmetic
Fried M.D., Jarden M. — Field Arithmetic

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Название: Field Arithmetic

Авторы: Fried M.D., Jarden M.

Аннотация:

ield 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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third Edition

Год издания: 2008

Количество страниц: 815

Добавлена в каталог: 04.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_{\iota, d}$-field      453
$C_{\iota}$-field      453
$e$-basic statement      551
$e$-cycle      315
$e$-free (field)      379
$g$ - Hilbertian      248
$G$-extension      294
$I$-cover      568
$K$- curve      173
$K$-algebraic set (projective)      185
$K$-basic (constructible set)      424
$K$-birational (varieties)      178
$K$-closed subsets      172
$K$-components (projective)      185
$K$-constructible set      423
$K$-derivation      48
$K$-hypersurface      174
$K$-isomorphic (curves)      96 97
$K$-isomorphism      180
$K$-morphism      180 186
$K$-normal (point)      96
$K$-place      20
$K$-rational (point)      178
$K$-rational map      178 186
$K$-variety      173
$K$-variety (projective)      185
$L$-rational point      188
$L$-series      122
$m$-ary variable symbols      700
$m$-stationary      676
$n$-adic structure      700
$n$-adic theories      700
$n$-dimensional projective space      185
$n$-imperfect      45
$n$-track      672
$p$ - Sylow group      522
$p$-adic integers      13
$p$-adic numbers (field of)      61
$p$-basis      44
$p$-cover      529
$p$-embedding problem      529
$p$-independent      44 45
$p$-projective      528
$P$-stratification      424
$S$-rank function      583
$T$-existentially closed (model)      658
$T$-extension      656
$X$-stable      294
$\infty$-imperfect      45
$\mathbb{Q}$-central (function)      740
$\mathcal{C}$-embedding problem      503
$\mathcal{C}$-homogeneous      615
$\mathcal{C}$-homogeneous cover      633
$\mathcal{C}$-projective      503
$\mu$-independent      370
$\omega$-free      652 752
$\sigma$-additivity      363
$\sigma$-algebra      363
${\L}$o$\check{s}$      142
Abelian extension      294
Abelian pro-$p$ groups      308
Abelian profinite      345
Abhyankar      70
Abhyankar's conjecture      70
Absolute Galois group      12
Absolute norm (of a prime ideal)      112
Absolute value      238
Absolutely converges(infinite product)      80 92
Absolutely irreducible (polynomial)      43
Absolutely irreducible (variety)      175
Abstract variety      189
Accessible      626
Ackermann      158
Ackermann function      158
Additive absolute value      278
Adele      64
Adler - Kiefe      670
Admissible      541
Admissible (ideal)      123
Affine $n$-space $\mathbb{A}^{n}$      172
Affine plane      95
Affine plane curve      95
Algebraic function field of one variable      52
Algebraic set      172
Algebraically independent (fields)      40
Algebraically independent (set)      40
Almost all      146
Almost contained (sets)      140
Almost equal (sets)      140
Almost full      542
Amalgamation property      656
ample      335
Arason - Fein - Schacher-Sonn      307
Archimedean (absolute value)      239
Arithmetic      706
Arithmetic progression      241
Arithmetical primes      280
Arithmetically definable      707
Artin      41 64 76 130 494 537 738
Artin - Schreier extension      29
Artin reciprocity law      124
Artin symbol      113 709
Atomic formula (of $\mathcal{L}_{n}$)      700
Atomic formulas      133
Ax      141 148 162 191 200 207 209 217 218 381 401 447 448 449 450 452 453 456 524 759
Ax - Roquette      196
B$\ddot{u}$chi      682
B$\hat{o}$cher      744
Bary - Soroker      613
Basic field      172
Basic functions      402
Basic sets      402
Basic statement      551
Basis (of a free abstract group)      346
Basis (of a free pro-$\mathcal{C}$ group)      348
Bauer      130 236
Beat      671
Beckmann - Black      760
Beckmann - Black Problem      565
Bell - Slomson      145 148
Bensimhoun      493
Bertini - Noether      169 171 179
Bezout ring      276
Bijective (polynomial function)      477
Binz - Neukrich - Wenzel      362 542
Birational equivalence (varieties)      178
Birationally equivalent (varieties)      178
Block (of a permutation group)      474
Bombieri      94 743
Boolean algebra of sets      140
Boolean algebra, generated by a family      140
Boolean polynomials      140
Borel - Cantelli      372
Borel field      362
Borevich- Shafarevich      61
Bottom theorem      385
Bounded (degrees)      417
Bounded (occurence of a variable)      133
Bounded minimum operator      157
Bourbaki      24 25 226
Branch point      214
Brandis      402 525
Brink      320 328
Burnside      206 477 495
Canonical class      55
Canonical divisor      55
Caratheodory      365
Carlitz's Conjecture      489
Cartesian product      182
Cartesian square      400
Cassels - Fr$\ddot{o}$hlich      21 32 62 63 65 206 239 241 314 363 381 469 470 483 485 742
Cauchy sequence      61
Center (of a divisor)      97
Center (of a prime divisor)      57
Central (function)      740
Central simple ($K$-algebra)      208
Chaevalley      76
CHARACTER      740
Character (of a finite abelian group)      122
Characteristic (subgroup)      330
Characteristic function      156
Chatzidakis      401 580 593 595 603 633 789
Chebotarev      130
Chebotarev density theorem      114
Chebyshev polynomials      479
Chebyshev's inquality      373
Cherlin      383
Cherlin - Jarden      706 707
Cherlin-v. d. Dries- Macinty re      453 542 560 690 697
Chevalley      24 64 76 423 455
Chevalley - Warning      455
Class number      77
Class of divisors      53
Classical Hilbertian fields      242
Coefficients (of an element in $\mathbb{Z}[H]$)      475
Cofinite      143
Cohen - Fried      490
Cohn      188
Cohomological dimension      210
Colliot - Th$\acute{e}$l$\grave{e}$ne      230 243 593
Commutator      309
Commutator subgroup      310
Compactness Theorem      144
Compatible (maps)      1 2
Complement (of a closed subgroup)      524
Complementary Galois stratification      719
Complementary module      65
Complete (measure)      365
Complete (theory)      152
Complete (valued field)      61
Completeness (of projective varieties)      186
Completion      61
Components (of a $k$-closed set)      174
Composition factor      326
Composition series      688
Compositum (of places)      23
Computes (a function)      672
concurrent      271
Conductor (of a ring extension)      100
Cone      272
Congruence test      132
Conjugacy domain of subgroups      710
Conjunction symbol      133
Consequence      149
Conservative (function field of one variable)      393
Conservative (function field of several variables)      392
Consistent      152
Constant      52 134
Constant field extension      59
Constant symbols      132
Constant terms      153
Continuous set theoretic section      9
Contradiction (formula)      152
Converge to one (subset)      338
Convergent to one (map)      346
Converges (infinite product)      80
Convex      274
Convex hull      280
Coordinate ring (of a $K$-basic set)      424
Coordinate ring (of a $K$-variety)      173
Coordinate ring (of a curve)      96
Coordinate ring (over $\mathbb{Z}[k^{-1}]$)      732
Corank (of a field)      439
Corvaja - Zannier      266 289
Cossey - Kegel - Kov$\acute{a}$cs      542
covers      513
Crossed homomorphism      526
Cusp      394
Cyclotomic (extension)      121
D$\grave{e}$bes      566 593
D$\grave{e}$bes - Haran      236 758
Data for being algebraically closed      662
Davenport      466
Davenport (Problem)      753
De - Morgans's laws      164
Decidable theory      159
Decision procedure      159
Decomposable      471
Decomposition factor (of a polynomial)      485
Decomposition field (of a place)      110
Decomposition field (of a prime ideal)      107
Decomposition group      25
Decomposition group (of a place)      110
Decomposition group (of a prime ideal)      107
Decomposition group condition      564
Dedekind      63 464
Dedekind domain      32
Dedekind zeta function      124
Deduction Theorem      151
Deductively close      150
Defined (absolutely irreducible $K$-variety)      175
Defined over K (scheme)      189
Degree (of a curve)      95
Degree (of a divisor)      53
Degree (of a field extension)      519
Degree (of a polynomial function)      478
Degree (of a prime divisor)      52
Degree (of a rational map)      178
Degree (of a stabilizing base)      391
Deligne      94
Denef - Jarden - Lewis      460
Denef - Loeser      729
Density property      397 751
Dentzer      306
Derivation      48
Deuring      53 54 55 59 60 61 76 130 210
Diamond theorem      260
Dickson polynomial      480
Different      67
Different (of a ring extension)      112
Different exponent      65
Differential      54 64
Dihedral group      472
Dimension (of a $K$-variety)      173
Dimension (of a constructible set)      423
Dimension (of a ring)      283
Dimension Theorem      174
Directed (family of subsets)      6
Directed (family)      341
Directed partially ordered set      1
Dirichlet      114 130
Dirichlet density      113
Discrete (valuation)      21
Discriminant (of a polynomial)      108
Discriminant (of a ring extension)      112
Discriminant (of an element)      109
Distinct (valuations)      20
Divides (supernatural number)      520
Divisor      52
Divisor (of a differential)      55 64
Divisor of poles      52
Divisor of zeros      52
Dixon      636 639
Dixon - Pyber - Seress-Shalev      358
Dixon-du.Sautoy - Mann - Segal      539
Domain      134
Domain of definition (of a rational map)      178
Dominant (rational map)      178
Douady      338
Double implication symbol      133
1 2 3 4
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