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Hida H., Fulton W. (Ed) — Modular Forms and Galois Cohomology
Hida H., Fulton W. (Ed) — Modular Forms and Galois Cohomology

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Название: Modular Forms and Galois Cohomology

Авторы: Hida H., Fulton W. (Ed)

Аннотация:

This book provides a comprehensive account of a key, perhaps the most important, theory that forms the basis of Taylor-Wiles proof of Fermat's last theorem. Hida begins with an overview of the theory of automorphic forms on linear algebraic groups and then covers the basic theory and recent results on elliptic modular forms, including a substantial simplification of the Taylor-Wiles proof by Fujiwara and Diamond. He offers a detailed exposition of the representation theory of profinite groups (including deformation theory), as well as the Euler characteristic formulas of Galois cohomology groups. The final chapter presents a proof of a non-abelian class number formula.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 354

Добавлена в каталог: 23.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr{C}$-chain map      170
$\mathscr{C}$-injectivity      166
$\mathscr{C}$-projectivity      169
(p-adic) cyclotomic character      9
Abelian category      162
Abelian extension      2
Absolutely irreducible module      31
Actin reciprocity law      8
Additive category      159 161
Adele ring      2 65
Adelic modular form      75
Adjoint L-function      267
Adjoint representation      255
Arithmetic Frobenius      111
Arithmetic Hecke characters      11
Artinian module      23
Augmentation      173
Automorphic induction      18
Base-change      18
Base-change map      297 304 306
Brauer — Nesbitt theorem      38
Category      154
Chain map      164
Characteristic ideal      291
Characteristic power series      249 291
Class formation      206
Class number formula      284
Co-tangent space      59
Coboundary      182
Cocycle      182
Coimage      161
Cokemel      161
Compatible system      12 13
Complete intersection      129
Completed tensor product      261
Completely reducible module      32
COMPLEX      170
Conductor of a Hecke character      73
Conductor of a Hecke eigenform      102
Congruence module      277
Congruence module, cohomological      282
Congruence module, higher      277
Connection map      173
Continuous cohomology      183
Contragredient      111
Contravariant      155
Control theorem      93 309
Covariant      155
Critical value, motive      246 256 269
Cup product      197
Cuspidal cohomology group      270 312
Degree of chain maps      170
Density theorem      35
Derivation      262
Differential      262
Differential module      276
Direct product      160
Direct sum      160
Discrete module      189
Duality theorem      97
Eisenstein series      18
Equivalence of cusp forms      102
Euler characteristic      227 231
Extension group      154 162
Extension product      176
Final object      160
Finite-group cohomology      180
Flat case      137
Flat Galois representation      121
Frattini condition      62
Frobenius element      108
Frobenius reciprocity      40
Full subcategory      155
Fully faithful      156
functor      155
Functorial      157
Geometric Frobenius      111
Global duality theorem      216 218
Global Euler characteristic      231
Gorenstein algebra      286
Graded module      170
Grothendieck group      39
Group algebra      34
Hasse — Weil L-function      3
Hecke algebra      80
Hecke algebra, universal p-ordinary Hecke algebra      292
Hecke character      7
Hecke eigenform      10 1
Hecke L-function      12
Higher congxuence module      277
Holomorphic cusp forms      64
Homotopy equivalence      173
inclusion      160
Induced representation      13 40
Inflation map      192
Inhomogeneous resolution      181
Initial object      160
Injective presentation      167
Injective resolution      173
Injectivity      162
Integrality theorem      88
Invariant      206
Invariant differential operators      10
Irreducible module      31
Iwasawa algebra      54
Kaehler differential      262
Kernel      161
Koszul complex      287
L-function, adjoint L-function      267
L-function, Hecke L-function      12
L-function, non-abelian L-function      13
Local duality theorem      212 214
Local Euler characteristic      227
Long Exact Sequence      193
Long extension sequence      176
Maximal p-group quotient      28
Maximal p-profinite quotient      28
Minimal case      139
Modular curve      3
Modular form      14
Morphism      154
n-coboundary      182
n-cocycle      182
Nakayama's lemma      30
Nearly ordinarity datum      240
Nearly ordinary      240 260
Neben      4
New form      103
Noetherian module      23
Non-abelian L-function      13
Number field      2
Object      154
Obstruction class      204
Old form      103
Ordinary      107
p-adic cyclotomic character      9
p-Frattini condition      62
p-ordinary      107
p-ordinary couple      119
Parabolic cohomology      273
Petersson inner product      104
Poitou- Tate exact sequence      220
Pontryagin dual      98
Prime-to-p profinite group      28
Primitive form      102
Profinite group      24
Projection      160
Projective limit      25
Projective presentation      169
Projectivity      169
Pseudo-isomorphism      248
Pseudo-representation of Taylor      50
Pseudo-representation of Wiles      46
Pure motive      245
q-expansion principle      92
Radical      29
Reciprocity law      1
Reciprocity map      206
Regular motive      237
Regular sequence      286
Regularity condition      118 122
Representable      157
Residual representation      115
Resolution      173
Restriction map      184
S-class formation      215
Schur's lemma      34
Selmer case      13 7
Selmer datum      240
Selmer group      237 239 241
Semi-simple module      32
Semi-simplification      40
Shimura — Taniyama conjecture      4
Snake lemma      171
Standard resolution      180
Strict case      13 7
Strict equivalence      51
Strong approximation theorem      65 68
Strong multiplicity one theorem      103
Subcategory      155
Table of categories      155
Tangent space      59 60
Tate cohomology      185
Tate — Shafarevich group      220
Taylor — Wiles system      128
Teichmliller lift      52
Theorem of Artin      41
Theorem of Faltings      122
Theorem of Tate      140 208
Theorem of Wedderburn      31
Theorem of Weil      12
Topological group      24
Transfer map      184
Transgression map      197 199
Unicity-lemma      157
Universal couple      51 119
Universal deformation ring      51
Universal p-ordinary Hecke algebra      292
Universal pseudo-representation      58
Universal representation      51
Unramified character      12
Unramified representation      13
Versal couple      119
Weight      4 245
Zero object      160
Zero-map      160
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