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Авторизация |
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Поиск по указателям |
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Diamond F., Shurman J. — First Course in Modular Forms |
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Предметный указатель |
-adic cyclotomic character 379
-adic integer 373
-adic Tate module of a modular curve 386
-adic Tate module of an elliptic curve 382
-adic Tate module of the curve xy = 1 373
-adic Tate module, associated to 389
-adic integers 375
-adic numbers 375
Abelian variety associated to an eigenform 241
Abel’s theorem 84 214
Absolute Galois group of Q 376
Addition law of elliptic curves, algebraic 254 312
Addition law of elliptic curves, geometric 253 312
Adjoint 183
Admissible change of variable 251 311
Affine plane 252
Algebraic closure of a field 250
Algebraic curve, affine 258
Algebraic curve, nonsingular 258
Algebraic curves, isomorphic 263
Algebraic curves, isomorphic over k 264
Algebraic element over a field 250
Algebraic field extension 250
Algebraic integer 231
Algebraic number 230
Algebraically closed 231
Algebraically closed field 250
Artin’s conjecture 395
Automorphic form of weight k 72
Base point 214
Bernoulli number 9 134
Bernoulli number of 135
Bernoulli polynomial 134
Bezout’s Theorem 252
Birational equivalence of algebraic curves 264
Birch and Swinnerton — Dyer conjecture 362
Canonical divisor on a Riemann surface 84
Commensurable congruence subgroups 164
Compatibility condition for meromorphic differentials on a Riemann surface 78
Complex multiplication 30
Complex torus 25
Conductor of a Dirichlet character 117
Conductor of a normalized eigenform 198
Conductor of an elliptic curve, algebraic 324
Conductor of an elliptic curve, analytic 292
Congruence subgroup 13
Conjugate function fields 264
Coordinate ring of an algebraic curve 257
Cubic Reciprocity Theorem 160
Curves–Fields Correspondence, Part 1 264
Curves–Fields Correspondence, Part 2 265
Cusp form of weight k 6
Cusp form of weight k with respect to a congruence subgroup 17
Cusp of a modular curve 58
Cusp of a modular curve, irregular 89
Cusp of a modular curve, regular 89
Cusp of an elliptic curve 314
Cyclic quotient isogeny 27
Decomposition group 369
Decomposition group, absolute 377
Decomposition index 367
Dedekind eta function 19
Degree of a map of Riemann surfaces 65
Degree of a morphism of algebraic curves 269
Degree of a morphism, inseparable 320
Degree of a morphism, separable 320
Degree-0 divisors of an algebraic curve 270
Desingularizing an algebraic curve 264
Dirichlet character, modulo N 116
Dirichlet character, primitive 117
Dirichlet character, trivial 116
Dirichlet L-function 121
Dirichlet’s Theorem on Arithmetic Progressions 370
Discriminant of a quadratic number field 367
Discriminant of a Weierstrass equation 250 310
Discriminant, function on 6
Divisor group of an algebraic curve 269
Divisor on a Riemann surface 83
Double coset 103 164
Double coset operator as map of Picard groups 227
Double coset operator on Jacobians 228
Dual isogeny 28
Eichler — Shimura relation 354
Eigenform 186 195
Eigenform, normalized 195
Eigenspace of 119
Eisenstein series of weight 2 18
Eisenstein series of weight 2, normalized 19
Eisenstein series of weight k 4
Eisenstein series of weight k for a lattice 32
Eisenstein series of weight k, normalized 10
Elliptic curve over a field of characteristic 0 251
Elliptic curve over an arbitrary field 310
Elliptic curve, complex 35
Elliptic curve, ordinary 313
Elliptic curve, supersingular 313
Elliptic curve, universal 282 311
Elliptic point of a congruence subgroup 48
Enhanced elliptic curve for 38
Enhanced elliptic curve for 37
Enhanced elliptic curve for 37
Enhanced elliptic curve for , algebraic 301
Enhanced elliptic curve for , complex algebraic 301
Equivalence of Galois representations 379 380
Euler product 200
Exceptional points of a map 65
Factor of automorphy 14
Faltings’s Isogeny Theorem 362
Fermat’s Last Theorem 396
Field extension, inseparable 319
Field extension, purely inseparable 319
Field extension, separable 319
Fontaine — Mazur — Langlands Conjecture 395
Forward change of variable formula 218
Forward map of Jacobians 218
Forward map of Picard groups 220
Four squares problem 11
Fourier transform 9 143
Fourier transform, finite 150
Free Q-module on the points of a modular curve 86
Frobenius element of a Galois group 369
Frobenius element, absolute 377
Frobenius map on 317
Frobenius map on an algebraic curve 318
Function field of an algebraic curve 257
Function field over k 264
Functional equation of 120
Functional equation of 121
Functional equation of L(s, f ) 204
Fundamental domain for 54
Galois representation, -adic 378 380
Galois representation, associated to 389 390
Galois representation, associated to 387 388
Galois representation, associated to an elliptic curve 383
Galois representation, associated to f 390 391
Galois representation, geometric 395
Galois representation, modular 391 395
Galois representation, odd 393
Galois representation, unramified 380
Gamma function 120
Gauss sum of a Dirichlet character 118
Generating function 11 134 179
Genus 65
Genus formula 68
Genus of a modular curve 62
Global minimal discriminant of an elliptic curve 323
Hecke algebra over C 234
Hecke algebra over Z 234
Hecke operator 169
Hecke operator , four compatible notions of 175
| Hecke operator d (diamond operator) 169
Hecke operators on Jacobians 229
Hilbert basis theorem 266
Holomorphic at 3 16
Homology group of a Riemann surface 213
Hurwitz zeta function 135
Hyperbolic measure on H 181
Igusa’s Theorem 348
Inertia group 369
Inertia group, absolute 377
Integrally closed 232
Invariant of a Weierstrass equation 250 310
Inverse limit 373
Inverse Mellin transform 147
Isogeny 27 244
Isomorphism of algebraic curves 263
Isotropy subgroup 48
Jacobian of a modular curve 227
Jacobian of a Riemann surface 214
K-points of E 254
Kronecker symbol 367
Krull intersection theorem 342
Krull topology 377
L-function of a modular form 200
L-function of an elliptic curve (Hasse — Weil) 361
Lattice in C 25
Legendre relation 138
Level of a congruence subgroup 13
Linear space of a divisor on a Riemann surface 84
Lipschitz formula 147
Local ring of an algebraic curve at a point 259
Local ring of the Hecke ring 239
Localization of at 329
Localization of Z at p 334
Maximal ideal of the local ring at a point 259
Mellin transform 136 145 204
Meromorphic differential on a Riemann surface 78
mod representation 385
mod representation, modular 395
Modular curve 38
Modular form of weight k 4
Modular form of weight k with respect to a congruence subgroup 17
Modular function 7
Modular group 1
Modular invariant 7
Modular parameterization of an elliptic curve 63
Modularity Theorem, strong Version 362
Modularity Theorem, strong Version R 392
Modularity Theorem, Version 246
Modularity Theorem, Version 356
Modularity Theorem, Version 294
Modularity Theorem, Version 215
Modularity Theorem, Version 293
Modularity Theorem, Version 63
Modularity Theorem, Version 292
Modularity Theorem, Version L 362
Modularity Theorem, Version R 392
Moduli space 38
Moduli space for , algebraic 301
Moduli space for , complex algebraic 301
Moebius function 113
Mordell — Weil theorem 254
Morphism of algebraic curves 263
Morphism of algebraic curves, defined over a field 264
Morphism, inseparable 319
Morphism, purely inseparable 319
Morphism, separable 319
Multiplicity One property of newforms 196
Multiply-by-integer isogeny 27
N -torsion subgroup of a complex torus 30
N -torsion subgroup of an elliptic curve 254
n-dimensional projective space over K 255
Nakayama’s Lemma 235
NEW 173
Newform 195
Newforms at level N 188
Node of an elliptic curve 314
Noetherian ring 266
Nonsingular, geometrically 251
Norm map of function fields 219
Normal linear operator 183
Nth division polynomials of an elliptic curve 254
Number field 231
Number field of a modular form 234
Number ring of a field 232
OLD 173
Oldforms at level N 187
Orthogonality relations 117
Orthogonality relations, modified versions 118
p-adic valuation 322
Perfect field 321
Perfect pairing 243
Period of an elliptic point 49
Petersson inner product 182
Picard group of a Riemann surface 214
Picard group of an algebraic curve 270
Poisson summation formula 9 144
Polynomial function on an algebraic curve 257
Power sum 133
Prime subfield of a field 312
Principal congruence subgroup of level N 13
Principal divisor 270
Profinite 374
Projective line 256
Projective plane over k 252
Pullback of function fields 217
Pullback of function fields of algebraic curves 265
Pullback of holomorphic differentials 218
Pullback of meromorphic differentials 77
Ramification degree 367
Ramification degree of a map of Riemann surfaces 65
Ramification degree of a morphism at a point 269
Ramified prime in a number field 367
Rational function defined over a field 263
Rational function on an algebraic curve 257
Rational integer 231
Rational map of elliptic curves 264
Reduction of a projective algebraic curve over Q at p 338
Reduction of an affine algebraic curve over Q at p 337
Reduction of an elliptic curve over Q, bad 323
Reduction of an elliptic curve over Q, bad, additive 323
Reduction of an elliptic curve over Q, bad, multiplicative 323
Reduction of an elliptic curve over Q, good 323
Reduction of an elliptic curve over Q, good, ordinary 323
Reduction of an elliptic curve over Q, good, supersingular 323
Representation number 11
Residue degree 367
Residue field 367
Reverse change of variable formula 221
Reverse map of Jacobians 222
Reverse map of Picard groups 224
Riemann surface 25 47
Riemann zeta function 4 121
Riemann — Hurwitz formula 66
Riemann — Roch theorem 84
Schwartz function 151
Serre’s conjecture 396
Strong Multiplicity One property of newforms 198
Sylvester matrix 232
Tangent line to an algebraic curve 259
Tchebotarov Density Theorem 371
Tensor product of a finitely generated Abelian group and a field 240
Theta function 143
Trace map of holomorphic differentials 221
Transcendental element over a field 250
Uniformizer at a point 260
Upper half plane 2
Valuation at a point 261
Variety 293
Weakly modular function of weight k 2
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