Reinmann H. — The semi-simple zeta function of quaternionic Shimura varieties :: Электронная библиотека попечительского совета мехмата МГУ

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Reinmann H. — The semi-simple zeta function of quaternionic Shimura varieties

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Название: The semi-simple zeta function of quaternionic Shimura varieties

Автор: Reinmann H.

Аннотация:

This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 144

Добавлена в каталог: 23.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$a(\wp)$       99
$Aut(\varphi)$       108
$a_{0}$       70
$A_{\iota}$       35
$b_{0}$       17
$cls(\theta)$       110
$C_{f}$       12
$C_{k}$       12
$C_{p}(\mathcal{K})$       130
$D^{'}$       32
$D^{\times}_{\delta \sigma}$       69 71
$D_{I}$       16
$d_{\iota}$       39
$d_{\sigma^{i}}$       110
$E^{\lambda}_{s}$       14
$e_{i}$       44
$Fr_{t}$       41 49 50
$F^{'}$       70
$f^{(j)}$       79
$f^{(j)}_{p}$       79
$f^{p}$       68
$F^{\bullet}_{\wp}$       85
$F^{\upsilon}$       64
$F_{0}$       70
$F_{i}$       64
$f_{\infty}$       79
$G^{ab}$       128
$G^{ad}$       128
$G^{der}$       128
$G_{t}$       36
$h_{D}$       9
$H_{h}$       60
$h_{K}$       10
$H_{t}$       33
$Isom(\varphi^{1},\varphi^{2})$       108
$I^{'}$       85
$J_{T}$       39
$J_{\theta}$       132
$K(\varphi)$       46
$k_{d}$       44
$L^{ss}_{p}(\pi, \varrho, s)$       86
$L^{ss}_{p}(\pi, \varrho^{\circ}, s)$       86
$L_{l}$       114
$m(\pi)$       79
$m(\pi, C)$       79
$M_{\bar{C}}$       13
$Nm_{\sigma}(\delta)$       72
$Nm_{\tau}(\delta^{'})$       72
$O_{B}$       17
$O_{D}$       17 70
$O_{h}(f)$       69
$P_{D}$       70
$q(l)^{L}$       115
$q^{'}$       70
$Q^{L}$       114
$Q_{i}$       64
$r^{'}$       71
$R^{k} \Psi \mathbb{Q}_{l}$       49
$R^{k}_{t,d}$       50
$R^{k}_{t}$       50
$R_{0}$       72
$r_{K}$       10
$R_{t,d}$       50
$S(\varphi)$       133
$Sh^{p}_{D}$       47
$Sh^{p}_{G}$       131
$Sh_{D,C}$       9
$Sh_{G,C$       11
$Sh_{G,C,Z}$       29
$TO_{\delta \sigma}(\Phi)$       69
$Tr^{ss}_{\wp}(X,j)$       67
$Tr^{ss}_{\wp}(\pi, \varrho^{\circ}, j)$       86
$W(\mathbb{F})$       22
$W^{'}_{E}$       2
$W^{'}_{\mathbb{Q}_{p}}$       84
$X^{'}_{t,i}$       43
$X^{'}_{t}$       43
$X^{p}(\varphi)$       131
$X_{p}(\varphi)$       132
$x_{t}$       41
$Y^{'}_{p}(\delta)$       62
$Y^{'}_{t}$       44
$Y^{p}(h)$       60
$Y_{D}$       38
$Y_{h}$       131
$Y_{p}(h)$       60
$Y_{t}$       43
$Z^{ss}_{p}(X,s)$       68
$Z^{ss}_{\wp}(X,s)$       67
$Z_{G}$       128
$Z_{t}$       33
$\alpha(A, \iota_{K})$       100
$\bar{c}$       12
$\bar{\mathbb{A}^{p}_{f}}}$       120
$\beta(A, \iota_{K}, B|K)$       94
$\beta(\Psi)$       96
$\Delta_{i}$       31
$\eta_{p}$       42
$\eta_{T}$       35
$\gamma$       106
$\iota_{t}$       35
$\kappa(p_{i})$       50
$\kappa_{i}$       46
$\lambda_{t}$       35
$\matfrac{T}_{D}$       34
$\mathbb{B}(G)$       110
$\mathbb{D}$       117
$\mathbb{F}$       22
$\mathbb{Q}^{nr}_{p}$       22
$\mathbb{S}$       9
$\mathbb{Z}^{nr}_{p}$       22
$\mathcal{A}$       78
$\mathcal{B}$       11
$\mathcal{B}(G,K)$       128
$\mathcal{B}^{'}$       96
$\mathcal{B}_{cris}$       91
$\mathcal{C}(G,K)$       130
$\mathcal{D}$       109
$\mathcal{D}_{n}$       109
$\mathcal{F}$       132
$\mathcal{F}_{t}$       41
$\mathcal{H}(B)$       111 124
$\mathcal{J}_{D}$       33
$\mathcal{K}$       30
$\mathcal{K}_{n}$       41
$\mathcal{M}_{\bar{C}}$       48
$\mathcal{P}_{l}(Z)$       124
$\mathcal{P}_{\omega}(Z)$       127
$\mathcal{V}$       9
$\mathcal{V}_{K}$       9 17
$\mathcal{Z}$       9 70
$\mathcal{Z}(y)$       46
$\mathcal{Z}(\mathfrac{a})$       23

$\mathcal{Z}^{+}(\mathfrac{a})$       23
$\mathcal{Z}^{-}(\mathfrac{a})$       23
$\mathcal{Z}_{0}$       22
$\mathcal{Z}_{1}$       46
$\mathcal{Z}_{t}(d)$       46
$\mathfrac{Q}$       120
$\mathfrac{q}_{i}$       17
$\mathfrac{R}$       80
$\mathfrac{R}(t)$       60
$\mathfrac{R}^{'}(t)$       62
$\mathfrak{B}$       120
$\mathfrak{G}(l)$       114
$\mathfrak{G}^{\Delta}$       106
$\mathfrak{G}_{G}$       107
$\mathfrak{G}_{l}$       109
$\mathfrak{G}_{p}$       109
$\mathfrak{G}_{\infty}$       109
$\mathfrak{p}_{i}$       16
$\mu_{h}$       127
$\nu(l)^{L}$       115
$\nu(p)$       117
$\nu(p)^{L}$       117
$\nu(\infty)$       117
$\omega_{h}$       128
$\omega_{L^{'}|L}$       117
$\Phi$       65 70 132
$\Phi^{'}$       70
$\phi_{C}$       13
$\Phi_{\upsilon}$       64 70
$\pi$       17
$\pi_{C}$       49
$\Psi$       11 17
$\psi^{L}$       114
$\psi^{\Delta}$       117
$\psi_{h}$       128
$\psi_{\mu}$       123
$\Sigma$       22
$\tau$       11 72
$\theta(r^{'}, \pi)$       71
$\theta^{nr}$       110
$\tilde{X}(G, \mathcal(K))$       130
$\tilde{\mathbb{A}_{f}}$       91
$\underline{M}_{G,C,Z}$       29
$\underline{M}_{G,C}$       16
$\underline{\mathcal{M}}_{G,C}$       18
$\underline{\mathcal{M}}_{G,C}(t)$       41
$\upsilon_{0}$       70
$\varphi(\pi)$       84
$\varphi_{i}$       31
$\varrho$       83
$\varrho(L^{'}, \varepsilon)$       34
$\varrho(Q|K, Q^{'}|K, \Phi)$       93
$\varrho^{\circ}$       83
$\varrho_{p}$       84
$\widehat{D^{\times}}$       83
$\widehat{T}^{p}(A_{s})$       14
$\widehat{V}^{p}(A_{s})$       14
$\widehat{\mathcal{O}}_{x}$       22 30 51
$\widetilde{Sh}^{p}_{D}$       49
$\widetilde{Sh}_{D,C}$       49
$\widetilde{Sh}_{G,C}$       19
$\xi_{l}$       128
$\xi_{\infty}$       128
$^{L}D^{\times}$       83
Abelian scheme      14
Admissible filtration      66 68
Admissible homomorphism      4
Admissible model      59 135
Admissible morphism      54 131 134
Admissible set      29 46 51
Admissible set, minimal      29 46 51
Associated, elements      72 78
Associated, functions      75
Base change lift      76
C-class of isomorphisms      14
Class field theory      10 84
D      9 70
d(Z)      29 46
e      41
E(D)      9
E(K)      10
Element, $\sigma$ -semi-simple      72
Element, $\tau$ -semi-simple      72
f      9 70
Filtration, admissible      66 68
Filtration, monodromy      85 87
Filtration, Schmid      85
FR      48
G      11
Galois action      10 22 45 51
Galois action, twisted      22 23 27
Groupoid, affine algebraic      108
Groupoid, Dieudonne      109
Groupoid, kernel of      106
Groupoid, neutral      54 107 123 124
Groupoid, pseudo-motivic      120 134
Groupoid, quasi-motivic      120 123
Groupoid, special section of      106 108
inv(x,y)      130
Isogeny type      33 37
K      9 17
L      15 17
l(L)      114
L-function      1 88
L-function, semi-simple      5 67 86 88
L-group      83
Morphisms of groupoids      107
Morphisms of groupoids, equivalent      108 126
Morphisms of groupoids, equivalent algebraically      108
N      39
Orbital integral      69 72 76 78 79
Orbital integral, twisted      69 72 78
p-principal isogeny      14
R      117
Related measures      79
S(t)      49
Scheme      14
Semi-simple trace      67 82 86
Serre condition      123
Sheaf of type (L, $\mathcal{V}_{K}$ )      15
Shimura variety      1 9—11 131
Shimura variety, admissible model for      59 135
Shimura variety, as moduli scheme      6 14
Shimura variety, dimension of      3 4 88
Shimura variety, Galois twist of      6 13
Shimura variety, reduction of      21 50 106 127
Shimura variety, reduction of, good      30 52 59 88 135
Strict completion      22 48
Unramified conjugacy class      59 135
Vanishing cycles, sheaves of      5 49 51
Vanishing cycles, spectral sequence of      5 68
Weil — Deligne group      2 84
Zeta function      1 3—5 68 88
Zeta function, semi-simple      5 8 67 87 88

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