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Malle G., Matzat B.H. — Inverse Galois Theory
Malle G., Matzat B.H. — Inverse Galois Theory

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Название: Inverse Galois Theory

Авторы: Malle G., Matzat B.H.


(Springer Monographs in Mathematics) Inverse Galois Theory is concerned with the question: which finite groups occur as Galois Groups over a given field? In particular, this includes the question on the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations. Contents: The Rigidity Method.- Applications of Rigidity.- Action of Braids.- Embedding Problems.- Rigid Analytic Methods.- Appendix: Example Polynomials.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1999

Количество страниц: 436

Добавлена в каталог: 28.10.2008

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Предметный указатель
$H^{V}_{s}$-rigid class vector      210
$\mathcal{M}$-section      381
$\wp$-stable      85
(full) Artin braid group      178
(full) Hurwitz braid group      180
Accompanying Brauer embedding problem      329
Accompanying embedding problem      329
Admissible covering      364
Admissible subset      364
Affinoid analytic space      364
Algebraic fundamental group      4 187
Almost character      124
Arithmetic fundamental group      9 196
AV-rigid      63
AV-symmetric      63
AV-symmetrized irrationality degree      63
Axis of a pseudo-reflection      251
Belyi triple      99
Braid relations      180
Brauer embedding problem      317
Center of a pseudo-reflection      251
Central embedding problem      266
Clean Belyi function      17
Closed ultrametric disc      374
Coherent sheaf      367
Cohomologically trivial in dimension i      339
Compatible family      379
Concordance obstruction      342
Concordant embedding problem      329
Conformal orthogonal group      109
Conformal symplectic group      106
Connected rigid analytic space      365
Coroot      91
Cyclotomic character      14
Cyclotomic polynomial      115
Disclosed function field of one variable      13
Embedding problem      265
Existentially closed      386
Field of definition      18
Field of definition with group      18
Finite embedding problem      266
Finite morphism      372
First embedding obstruction      342
Frattini embedding problem      266
Full symmetry group      31 62
G-compatible family      381
G-realization      33
GA-realization      35
GAR-realization      278
General unitary group      104
Generating s-system      26
Geometric (proper) solution      266
Geometric embedding problem      266
Geometric field extension      8
Geometrically conjugate      123
Gluing datum      364
Good reduction modulo p      87
Green function      125
Group of geometric automorphisms      41
Hasse embedding obstruction      342
Hasse — Witt-invariant      309
Hilbertian field      264
Hilbertian set      264
Homology      97
Homomorphism ramified in      392
Induced cover      374
Irrationality degree      28
j-th braid orbit genus      211
k-rational class vector      296
k-symmetric class vector      296
Kernel of an embedding problem      266
Large field      388
Lusztig series      123
Morphism of rigid analytic spaces      364
Non-split embedding problem      266
Normalized structure constant      36
Open ultrametric disc      374
Orthogonal group      107
Orthogonal group of minus type      113
Orthogonal group of plus type      109
Pairwise adjusted      383
Parametric solution of an embedding problem      266
Primitive linear group      97
Primitive prime divisor      115
Primitive translate      53
Profinite Hurwitz braid group      188
Projective profinite group      272
Proper solution (field) of an embedding problem      266
Pseudo algebraically closed      225
Pseudo-reflection      97
Pure Artin braid group      178
Pure Hurwitz braid group      180
Quasi-central element      129
Quasi-determinant      112
Quasi-p-group      396
r-fold uncomplete product      178
r-fold uncomplete symmetric product      178
Rational class vector      28
Rational subset      363
Rationally rigid class vector      28
Reduced braid orbit genera      241
Reflection      97
Rigid $H^{V}_{s}$-orbit      210
Rigid $H^{V}_{\mathbb{S}}$-orbit      47 63
Rigid analytic space      364
Rigid braid cycle      243
Rigid class vector      28
Ring of holomorphic functions      363
Root      90
s-th V-symmetrized braid orbit genus      231
Scholz embedding problem      352
Scholz extension      352
Scholz solution      352
Schur multiplier      222
Second embedding obstruction      342
Semiabelian group      276
Semirational class      41
Shape function      222
Socle of an $\ell$-Galois extension      352
Solution field of an embedding problem      266
Solution of an embedding problem      265
Sphere relations      181
Spinor norm      107
Split embedding problem      266
Strictly non-degenerate quadratic form      310
Symmetry group      31 62
Symplectic group      106
t.i.-property      155
Tate algebra      362
Thick normal subgroup      184
Transference      326
Transvection      97
Trivial cover      374
Twisted structure sheaf      368
Uniform function      123
Unipotent character      123
Uniquely liftable      295
Unirational function field      199
Universally central embeddable Galois extension      306
Unramified      186
Unramified rational place      219
V-configuration      47 228
V-rigid class vector      47
V-symmetric      31
V-symmetrized braid orbit      209
V-symmetrized irrationality degree      31
Voelklein's base group      249
Wreath extension      326
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