van der Geer G. — Hilbert modular surfaces :: Электронная библиотека попечительского совета мехмата МГУ

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van der Geer G. — Hilbert modular surfaces

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Название: Hilbert modular surfaces

Автор: van der Geer G.

Аннотация:

Over the last 15 years important results have been achieved in the field of Hilbert Modular Varieties. Though the main emphasis of this book is on the geometry of Hilbert modular surfaces, both geometric and arithmetic aspects are treated. An abundance of examples - in fact a whole chapter - completes this competent presentation of the subject. This Ergebnisbericht will soon become an indispensible tool for graduate students and researchers in this field.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 291

Добавлена в каталог: 14.05.2005

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Предметный указатель

(-2)-configuration      162
(-2)-curve      162
Abelian scheme with real multiplication      223
Adelic formulation      25
Algebraic cycle      155
Algebraic cycle, space      229
Algebraic cycle, stack      229
Arithmetic cycle      89
Arithmetic cycle, genus      46 58 65
Baily — Borce compactification      44 236
Betti number      58
Bounciary point (of convex hull)      32
Canonical divisor (class)      159 178
Canonical divisor (class), map      188
Castelmuovo's criterion      162
Chern class      45 66
Chern class, cycle      63 66
Chern class, number      61
CM-type      248
Coarse moduli scheme      228
companion      145
Complete $\mathbb{Z}$ -moduIe      28
Content      103
Continued fraction      37
Convex hull      32
Cusp      6 231
Cusp, form      18
Cusp, singularity      41
Cuspidal cohomology      125 245
CYCLE      35 155 240 243
Descent data      229
Diagonal surface      191
Dimension formula (for cusp forms)      71
Discriminant (of a quadratic form)      103
Discriminant (of a quaternion algebra)      90
Doi — Naganuma lifting      122 136
Dual (of )      130
Dual (of abelian scheme)      224
Eisenstein series      19
Eisenstein series, series (non-holomorphic)      22 49
Elliptic      15
Elliptic configutation      164
Elliptic fixed point      14 106
Elliptic surface      160
Enriques surface      160
Euler number      60
Euler number, product      126
Exceptional curve (of 1st kind)      159 167
Extended Hilhert modular group      11
Fixed point      14
Fundamental discriminant      2
Fundamental discriminant, domain      9
Fundamental discriminant, group      81
Galois involution      116
General type      161
Generating series      121 133
Genus      3
Genus, character      3
Geometric genus      58
Grassmannian      100 211
Hecke algebra      126
Hecke algebra, correspondence      126
Hecke algebra, operator      126
Hilbert modular form      17 234
Hilbert modular form, modular group      5
Hilbert modular form, modular surface      44
Hilbert modular form, modular variety      44
Hilbert — Blumenthal      2
Hirzebruch proportionality principle      61
Hirzebruch — Zagier class      128
Hirzebruch — Zagier class, cycle      245
Hodge cycle      240 243
Hodge cycle, filtration      124
Hodge cycle, structure      147
Hodge — Riemann bilinear relation      146
Holomorphic projection principle      115
Honestly elliptic surface      160
Humbert surface      205
Hurwitz — Maass-extension      10 12
Intersection (co)-homology      124 132
Intersection (co)-homology, number      110 142

Intersection (co)-homology, point      102
Irregularity      58
Jacobian (with real multiplication)      200
K-3 surface      160
Kodaira dimension      159
Kodaira's list      163
Koechei principle      18 30 235
L-series      22 137 140 149
Lefschetz number      155
Length (of complete $\mathbb{Z}$ -module)      47 70
Local Chern cycle      63
Meyer's theorem      48
Minimal model      160
Miyaoka — Bogomolov inequality      189
Modular curve      86 89
Modular curve, embedding      209
Modular curve, form      17 234
Modular curve, form on $\Gamma_0(D)$       118
Modular curve, stack      227
Moduli space      222
Motive      145
Multiplicity-one-principle      145
Narrow ideal class group      12
Neron — Severi group      207
Noether's formula      46
Noether's formula, inequality      189
Noim-signature character      67
Oda's conjecture      122
Oda's conjecture, period relation      153
Ordered $\sigma$ -module      225
Oriented basis      37
Orthogonal group      252
Period (of continued fraction)      38
Period (of modular form)      146 147 152
Peterson product      18 19
Picard number      155
Pluri-genus      159
Poincare duality      144
Polarization module      205 225
Prime discriminant      2
Principal congruence subgroup      77
Proportionality principle      61
Quotient singularity      4 41
Rational surface      160
Rationality criterion      161
Real multiplication      207 223
Reduced quadratic irrationality      38
Resolution cycle      35
Riemann form      205
Rosati involution      207
Rotation factor      16
Satake compactification      44
Semi-abelian      230
Siegel upper half plane      206
Signature      47 48 65
Similitude norm      252
Skew-hermitian curve      88
Skew-hermitian curve, matrix      80
Special point      102
Spits      125
Strict class number      2 14
Strict class number, equivalence      2 12 28
Symmetric Hilbert modular group      11
Symmetric Hilbert modular group, homomorphism      225
Symmetric Hilbert modular group, space      100
Symplectic group      206
Tate character      242
Tate character, conjectures      239 244 257
Tate character, cycle      240 243
Theta series (of an indefinite form)      134
Totally positive      5 208
Troidal embedding      36
Twisted diagonal      85
Twisting      242 256
Type of a cusp      7
Volume      59 101
Volume form      59
Weight      17
Weight, filtration      124
Zeta function (of a complete $\mathbb{Z}$ -module)      50
Zeta function (of a number field)      59

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