Shimura G., Taniyama Y. — Complex multiplication of Abelian varieties and its applications to number theory :: Электронная библиотека попечительского совета мехмата МГУ

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Shimura G., Taniyama Y. — Complex multiplication of Abelian varieties and its applications to number theory

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Название: Complex multiplication of Abelian varieties and its applications to number theory

Авторы: Shimura G., Taniyama Y.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1961

Количество страниц: 159

Добавлена в каталог: 22.11.2009

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Предметный указатель

$\mathfrak{p}$ -basic system for a variety      99
$\mathfrak{p}$ -complete      82
$\mathfrak{p}$ -finite differential form      90
$\mathfrak{p}$ -finite rational mapping      85
$\mathfrak{p}$ -simple      89
$\mathfrak{p}$ -variety      82
$\mathrm{N}(\mathfrak{p})$ -th power endomorphism, homomorphism      110
a-multiplication      52
a-section point      63
a-transform      53
Abelian variety of type      see “Type”
Almost all (for all p)      100 126
Alternating form, defined by a divisor      21
Alternating form, defined by a theta-function      20
Ample (divisor, linear system)      26
Analytic coordinate system of an abelian variety      21
Analytic representation of $\mathscr{H}_0(A,B)$       21
Basic polar divisor      30
Basic system for a variety      99
Characteristic polynomial, roots of an element of $\mathscr{A}_0(A)$       2
Class of positive Hermitian forms      121 132
CM-type      44
Complex torus      19
Conductor of a Groessen-character      143 149
Conductor of an order      136
Defect for $\mathfrak{p}$       94 108
Differential form      5
Differential form of the first kind      8
Discrete place      79
Dual of a CM-type      71
Dual of an abelian variety      23
Equivalent $(\{\alpha,\rho\})$       121 132
Equivalent (Grossen-character)      143
Extension of a place      78 79
Field of moduli      29 236
Finite (differential form) along (or at) a subvariety      6
Finite (differential form) at a point of $\tilde{V}$       90
Functional equation      143 144 145
Grossen-character      142
Hasse's conjecture      145
Homomorphism of $(A,\imath)$       52
Homomorphism of $(A,\mathscr{C})$       28
Homomorphism of an abelian variety      1
Index of $(A,\imath)$       56
Invariant differential form      9 12
Involution of $\mathscr{A}_0(A)$ determined by a divisor      3
Irreducibility of the class-equation      128 130
Isogenous, isogeny      1
Isomorphism of $(A,\imath)$       52
Isomorphism of $(A,\mathscr{C})$       28
Isomorphism of $\mathscr{P}=(A,\imath,\mathscr{C})$       117
Isomorphism of an abelian variety      1
Jacobian variety      17 130
k-basic system for a variety      90
Kummer variety      35
l-adic coordinate system      2
l-adic representation of $\mathscr{H}_0(A,B)$       2
l-adic representation of a divisor      4
L-function with Groessen-character      143
Lattice in an algebra      52
Left invariant differential form      9
Local parameters      7 87
Modular function, elliptic      v 129 135
Modular function, Hilbert      v
Modular function, Siegel      29
Multiplication (a-)      52
Non-degenerate divisor      3 28

Normal lattice in an algebra      55
Normalized Kummer variety      35
Normalized theta-function      20
Open set of discrete places      100
Order in an algebra      52
Order of $(A,\imath)$       52
Picard variety      3 51
Place of a field      77
Point in $\tilde{V}$       83
Polar divisor      27
Polarizable, polarization      27
Polarized Abelian variety      27
Polarized abelian variety of type $(\mathrm{K}; \{\varphi_i \})$       117
Polarized abelian variety of type $(\mathrm{K}; \{\varphi_i \}; \mathrm{f}_0})$       118
Polarized variety      27
Primitive CM-type      68 72 73
Primitive Groessen-character      143
Principal $((A,\imath))$       56
Proper a-section point      63
q-th power enomorphism, homomorphism      4 5 66
Quotient of an abelian variety by a group of automorphisms      34
Rational representation of $\mathscr{H}_0(A,B)$       22
Reduced norm, trace, representation of a simple algebra      38
Reduction modulo of $\mathfrak{p}$ a cycle      80 81 83
Reduction modulo of $\mathfrak{p}$ a differential form      91
Reduction modulo of $\mathfrak{p}$ a function      85
Reduction modulo of $\mathfrak{p}$ a homomorphism      94
Reduction modulo of $\mathfrak{p}$ a rational mapping      85
Reduction modulo of $\mathfrak{p}$ an abelian variety      94
Reduction modulo of $\mathfrak{p}$ an abstract variety      83
Reduction modulo of $\mathfrak{p}$ an affine variety      79
Regular at a point of $\VEC{V}$ (birational mapping)      81
Regularly corresponding points      82
Representation of $\mathscr{H}_0(A,B)$ by invariant differential forms      17
Representation, analytic, of $\mathscr{H}_0(A,B)$       21
Representation, l-adic, of $\mathscr{H}_0(A,B)$       2
Representation, l-adic, of a divisor      4
Representation, rational, of $\mathscr{H}_0(A,B)$       22
Representative in $\tilde{V}$       83
Residue field of a place      77
Riemann form      19
Riemann form defined by a divisor      21
Riemann form defined by a theta-function      20
Riemann hypothesis for congruence zeta-functions      v 5
Ring of $\mathfrak{p}$ -integers      77
Section point (a-)      63
Simple (a point or a subvariety in $\tilde{V}$ simple on V)      81 83
Specialization over a place      78
Specialization over a place of a point      83
Specialization ring      31 78
Stickelberger's relation      130
Subvariety of a $\mathfrak{p}$ -variety      82
System of local parameters      7 87
Theta-function      20
Transform (a-)      52
Transpose of an element of $\mathscr{H}_0(A,B)$       3
Trivial place      78
Type $(\mathrm{F}; \varphi_1, \dots \varphi_n)$ or $(\mathrm{F}; \{\varphi_i \})$       43
Type $(\mathrm{K}; \{\varphi_i \}; \mathrm{f}_0; \mathfrak{b}})$ or $\mathfrak{R}(\mathfrak{b})$       131
Type $(\mathrm{K}; \{\varphi_i \}; \mathrm{f}_0})$       118
Type (F), $(\mathfrak{R})$       42 43
Variety in $\tilde{V}$       82
Weber's $\tau$ -function      135
Weierstrass' $\gamma$ -function      135
Weil's conjecture on $\mathrm{Z}(u; V/\kappa)$       144
Weil's conjecture on $\zeta(s; V/k)$       145
Zeta-function of a variety defined over a finite field      143
Zeta-function of a variety defined over an algebraic number field      144

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