Li K.-Z., Oort F. — Moduli Of Supersingular Abelian Varieties :: Электронная библиотека попечительского совета мехмата МГУ

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Li K.-Z., Oort F. — Moduli Of Supersingular Abelian Varieties

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Название: Moduli Of Supersingular Abelian Varieties

Авторы: Li K.-Z., Oort F.

Аннотация:

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to Äg.g/4Ü, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 116

Добавлена в каталог: 22.11.2009

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Предметный указатель

$(S/W)_{cris}$       5.3
$Aut(E^{g} \otimes K,\eta)$       4.10
$A_{1,1}$       5.6
$A_{K}$       5.2
$A_{R}$       7.9
$A_{U}$       7.6
$f \approx f^{'}$       4.6
$f \sim f^{'}$       4.6
$F_{s}$       2.3
$F_{X/S}$       2.3
$F_{X/S}^{n}$       2.3
$G[F^{n}]$       2.3
$G^{D}$       1.3
$G_{m,n}$       1.4
$G_{\eta}$       9.2
$G_{\mathcal{F}}$       2.4
$G_{\mathcal{F}}^{1}$       2.4
$H_{g}(1, p)$       4.6
$H_{g}(p, 1)$       4.6
$H_{mn}$       13.6
$H_{p}$       9.1
$j_{n}$       11.1
$n_{G}$       1.3
$N_{p}$       4.6
$O_{S/W}$       5.3
$Q_{\infty , p}$       1.2
$r_{i}$       12.2
$r_{mn}$       13.10
$Sym (\mathcal{F})$       2.4
$S^{0} M$       5.6
$S^{0} X$       1.8
$S_{0} M$       5.6
$S_{0} X$       1.8
$s_{i}$       12.2
$T_{g}$       9.3
$T_{\mu}$       9.11
$U^{\Theta}$       7.6
$V_{G/S}$       2.3
$W_{n}(R)$       5.3
$w_{\alpha}$       A.13
$W_{\eta}$       9.2
$X^{(p^{n})}$       2.3
$y_{i}$       3.1
$\alpha$ -group      2.4
$\alpha$ -rank      2.4
$\alpha$ -sheaf      2.4
$\alpha_{p}$       0.3
$\epsilon$       6.1
$\eta$       3.6
$\eta_{i}$       3.6
$\Gamma_{F}$       8.6
$\lambda$       4.2
$\langle , \rangle$       5.7 8.1
$\mathbb{D}$       5.4
$\mathcal{A}_{g, d, n}$       1.9
$\mathcal{A}_{g, d}$       1.9
$\mathcal{A}_{G}$       0.4
$\mathcal{B}_{g, d, \eta}$       11.5
$\mathcal{D}_{g, n}$       10.2
$\mathcal{D}_{g}$       10.2
$\mathcal{E}^{(p)}$       5.3
$\mathcal{F}$       2.4
$\mathcal{F}^{[p]}$       2.4
$\mathcal{L}_{f, \approx}$       8.5
$\mathcal{L}_{f, \sim}$       8.5
$\mathcal{L}_{g}(1, p)$       4.6
$\mathcal{L}_{g}(p, 1)$       4.6
$\mathcal{M}$       2.1
$\mathcal{N}_{g}$       7.6
$\mathcal{O}$       1.2
$\mathcal{P} L$       7.7
$\mathcal{P}_{g, \eta}$       3.7
$\mathcal{P}_{g, \eta}^{'}$       3.7
$\mathcal{P}_{G}$       3.9
$\mathcal{P}_{g}^{'}$       3.9
$\mathcal{Q}_{g}$       3.5
$\mathcal{Q}_{g}^{'}$       3.5
$\mathcal{Q}_{g}^{n}$       11.1
$\mathcal{S}_{g, d, n}$       1.9
$\mathcal{S}_{g, d}$       1.9
$\mathcal{S}_{g, d}(a \ge n)$       9.9
$\mathcal{S}_{g}$       0.3
$\mathcal{T}_{g}$       A.11
$\mathcal{T}_{\mu}$       9.9
$\mathcal{U}^{\Theta}$       4.11
$\mathcal{U}_{m}$       3.5
$\mathcal{U}_{m}^{\Theta}$       7.6
$\mathcal{V}_{m}$       9.3
$\mathcal{W}$       5.1
$\mathcal{W}_{n}$       5.1
$\mathfrak{B}_{g, d, \eta}$       11.5
$\mathfrak{C}_{K}$       5.2
$\mathfrak{C}_{s}$       1.3
$\mathfrak{C}_{S}^{1}$       1.3
$\mathfrak{D}_{g, n}$       10.3
$\mathfrak{F}$       8.5
$\mathfrak{j}$       2.3
$\mathfrak{N}_{g}$       7.6
$\mathfrak{N}_{g}^{\Theta}$       7.6
$\mathfrak{P}_{g, \eta}$       3.7
$\mathfrak{P}_{g, \eta}^{'}$       3.7
$\mathfrak{P}_{g}$       3.9
$\mathfrak{P}_{g}^{'}$       3.9
$\mathfrak{p}_{\eta}$       3.7

$\mathfrak{p}_{\eta}^{'}$       3.7
$\mathfrak{q}_{g}$       3.5
$\mathfrak{q}_{g}^{'}$       3.5
$\mathfrak{S}$       13.12
$\mathfrak{t}_{m}$       7.6
$\mathfrak{U}_{m}$       3.5
$\mathfrak{U}_{m}^{\Theta}$       7.6
$\mathfrak{V}_{m}$       9.3
$\mid \ \mid$       6.1 8.1
$\mu$       5.1
$\mu_{p}$       0.3
$\omega_{G/S}$       2.1
$\overline {a + bF}$       7.9
$\Phi$       8.7
$\Phi^{*} \mathcal{F}$       5.3
$\pi$       8.7
$\Psi$       4.2
$\rho_{i}$       3.1
$\Sigma$       5.1
$\theta$       3.7
$\theta_{\eta}$       8.7
$\tilde{M}$       5.7
$\varphi_{p} X$       1.4
A      5.2
a(-/V)      1.10
A(M)      5.2
A(X)      1.5
a-number (of a commutative group scheme)      1.5
a-number (of a Dieudonne module)      5.2
Absolute Frobenius      2.3
Adelic hermitian form      8.5
B      1.2
Barsotti — Tate group      1.4
Cartier dual      1.3
Crystal      5.3
d(G)      5.2
Dieudonne crystal      5.3
Dieudonne module (over S)      5.5
Dieudonne module (over W)      5.2
Dual Dieudonne module      5.9
e      1.2
Epimorphism      13.2
Equivalent ( $\mathcal{O}$ -hermitian forms)      4.6
Equivalent polarizations      4.2
f      1.2 5.2 8.1
Flag type quotient (FTQ)      3.2
Formal isogeny type      1.4
Garbage component      9.6
Generically flat      13.1
Genus (of a Dieudonne module)      5.2
Globally equivalent ( $\mathcal{O}$ -lattices)      4.6
G[n]      1.3
H      5.7
Infinitesimal group scheme      2.3
Isogenous      1.3
Isogeny (of p-divisible groups)      1.3
Isotropic flag type quotient (IFTQ)      3.9
J(u, v)      8.1
Lie(G/S)      2.1
m-truncated FTQ      3.5
Minimal isogeny      1.8
Ordiary elliptic curve      1.1
p-Divisible group      1.3
p-Lie algebra      2.5
PFTQ of Dieudonne modules (over S)      7.3
PFTQ of Dieudonne modules (over W)      6.2
Polarized flag type quotient (PFTQ)      3.6
Principal quasi-polarization      5.9
Quasi-equivalent ( $\mathcal{O}$ -hermitian forms)      4.6
Quasi-polarization (of G)      8.7
Quasi-polarization (of M)      5.9
Quasi-polarized Dieudonne module (over S)      7.2
Quasi-polarized Dieudonne module (over W)      5.9
R      12.2
R(u, v)      8.1
Rank (of a flat finite group scheme)      2.1
Relative Frobenius      2.3
Rigid FTQ      3.2
Rigid PFTQ      3.6
Rigid PFTQ of Dieudonne modules      6.2
S      12.2
S-PD thickening      5.3
Serre dual (of a p-divisible group)      1.3
Singular elliptic curve      A.1
Skeleton      5.7
Stratum      A.13
Strictly supersingular abelian scheme      13.3 13.8
Supergeneral abelian variety      1.7
Supergeneral Dieudonne module      5.6
Supersingular abelian scheme      13.11
Supersingular abelian variety      1.4
Supersingular Dieudonne module      5.6
Supersingular elliptic curve      1.1
Supersingular locus      1.10 13.12
Superspecial abelian variety      1.7
Superspecial Dieudonne module      5.6
Torelli locus      A.11
V      5.2
Verschiebung      2.3
w      5.1
W(K)      5.1
W(R)      5.5
Witt scheme      5.1
Witt vector      5.1

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