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Hida H. — Hilbert Modular Forms and Iwasawa Theory
Hida H. — Hilbert Modular Forms and Iwasawa Theory

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Название: Hilbert Modular Forms and Iwasawa Theory

Автор: Hida H.

Аннотация:

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for
researchers and graduate students entering this research area.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 400

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian scheme      296
Admissible representation      117
Affine formal scheme      3
Affine group scheme      91
Affine ring scheme      91
Affine scheme      87
Anticyclotomic character      379
Arithmetic      58 183
Arithmetic Hecke character      150
Arithmetic point      183
Arithmetic weight      182
Automorphic form      95
Automorphic manifold      99
Automorphic vector bundle      307
Balanced Selmer group      62—63 266
Balanced subgroup      170
Barsotti — Tate group      4
Characteristic ideal      8—9
CM field      152
CM type      152
Coarse moduli      290
Coinduction      12
Complete intersection      216
Complex multiplication      51
Cone decomposition      308
Congruence module      39 216
Congruence number      216
Conjecture of Greenberg      60
Conjecture of Mazur — Tati — Teitelbaum      59
Critical      24
Critical value      25—26
Crystalline case      45
Cyclic subgroup      319
Cyclotomic character      4
Cyclotomic point      183
Cyclotomic weight      183
Derivation      36
Double coset ring      110
Etale      89
Etale cyclic subgroup      319
Exceptional zero      59
expanding      119
Expanding semigroup      119
Faithfully flat morphism      88
Fiber functor      297
Fibered category      297
Fibered product      90
Finite morphism      88
Flat case      45
Flat deformation      44 210—211
Flat morphism      88
Flat nonordinary      210
Flat residual representation      44
Formal spectrum      3
Free action      97
Geometric Frobenius map      23
Good reduction      27
Hasse invariant      314
Hasse — Weil conjecture      24
Hecke algebra for GL(2)      336
Hecke eigenform      43
Hecke module      110—111
Hecke operator      43 103—104 109 132 136 167 182 218 320
Hodge filtration      20
Hodge — Tate filtration      26
Homological dimension      369
Igusa tower      315
Induction of an H-module      11
Initial Galois representation      31
Initial Hecke eigenform      174
Initial Neben character      174
Isogeny      324—325
Iwasawa module      4—5
Iwasawa's logarithm      60
Jacquet module      117
Jacquet — Langlands and Shimizu correspondence      114
Kahler differential      35
Left exact functor      88
Level $\Gamma(N)$-structure      300—301
Level $\Gamma_0(\mathfrak{N})$-structure      301
Level $\Gamma_1^1(\mathfrak{N})$-structure      301
Local complete intersection      37—38
Locally cyclotomic point, cyclotomic point      182—183
Locally cyclotomic weight      182—183
Maximal at p      328
Mazur's principle      229
Minimal vector      122
Minimal versal hull      253
Moduli scheme      290
Multiplicative reduction      27
Nearly ordinary character      32
Nearly ordinary Hecke algebra      182 338—339
Nearly p-ordinary character      185
Nearly p-ordinary eigenform      163
Nearly p-ordinary representation      26
Neben character      99
New form      114
New vector      122—123
Normalization of a formal scheme      56—57
Old component      237
Ordinary abelian scheme      299
Ordinary good reduction      27
Ordinary semi-abelian scheme      314
Ordinary semistable reduction      27
Picard functor      297
Picard scheme      297
Polarization      297
Polarization ideal      298
Positive majorant      141
Prime-to-p isogenies      328
Principal congruence subgroup      100
Properly discontinuous action      97
Pseudo-null module      9
Pseudo-representation of Wiles      14
Rationality conjecture      25
Real multiplication      296
Reflex field      324
Regularity condition      257 260
Representability      290
Representable      32—33
Schematic representation      291
Schemes      94
Selmer case      45
Selmer group, minus Selmer group, strict Selmer group      28
Semi-abelian scheme      310
Semistable reduction      27
Sheaf or line bundle of cusp forms      315
Shrinking semigroup      119
Simplicial cone      308
Smooth induction      118
Smooth morphism      88—89
Smooth representation      117
Smooth, etale morphism      94
Special (or Steinberg) representation      118 122
Split multiplicative reduction      27
Strict case      45
Supercuspidal representation      121—122
Symmetric isogeny      297
Tamely ramified prime      5
Tate curve      293
Tate module      27 295 299
Tate module prime-to-$\Sigma$      325
Tate period      65
Tate semi-abelian scheme      312
Tate twists      22
The theorem of St. Etienne      62
Theorem of Faltings      257
Theorem of Urban      55
Universal nearly p-ordinary Hecke algebra      238
Universal pseudo-representation      17
Unramified representation      73
Versal hull      253
Weil pairing      300—301
Weil restriction      93
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