Finite flat group schemes over local Artin rings

被引：1

作者：

Schoof, R ^{[1
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

来源：

COMPOSITIO MATHEMATICA | 2001年 / 128卷 / 01期

关键词：

group scheme; Hopf algebra; deformations;

D O I：

10.1023/A:1017560215203

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a local Artin ring with maximal ideal m and residue class field of characteristic p > 0. We show that every finite flat group scheme over R is annihilated by its rank, whenever m(p) = pm = 0. This implies that any finite flat group scheme over an Artin ring the square of whose maximal ideal is zero, is annihilated by its rank.

引用

页码：1 / 15

页数：15

共 50 条

[31] Finite groups of matrices over group rings
Cliff, G
Weiss, A
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (01) : 457 - 475
[32] Cohomology of finite group schemes over a field
Eric M. Friedlander
Andrei Suslin
Inventiones mathematicae, 1997, 127 : 209 - 270
[33] Cohomology of finite group schemes over a field
Friedlander, EM
Suslin, A
INVENTIONES MATHEMATICAE, 1997, 127 (02) : 209 - 270
[34] FINITE-GROUP SCHEMES OVER FIELDS
HOOBLER, RT
MAGID, AR
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 33 (02) : 310 - +
[35] FLAT CHAINS OVER A FINITE COEFFICIENT GROUP
FLEMING, WH
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 121 (01) : 160 - &
[36] ON THE STRUCTURE OF SOME MODULI SPACES OF FINITE FLAT GROUP SCHEMES
Hellmann, Eugen
MOSCOW MATHEMATICAL JOURNAL, 2009, 9 (03) : 531 - 561
[37] FINITE FLAT MODELS OF CONSTANT GROUP SCHEMES OF RANK TWO
Imai, Naoki
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (11) : 3827 - 3833
[38] Difference schemes of strength t over finite commutative rings
Castoldi, Andre G.
Martinhao, Anderson N.
Carmelo, Emerson L. Monte
dos Santos, Otavio J. N. T. N.
Perondi, Pablo H.
DISCRETE MATHEMATICS, 2024, 347 (10)
[39] On rational singularities and counting points of schemes over finite rings
Glazer, Itay
ALGEBRA & NUMBER THEORY, 2019, 13 (02) : 485 - 500
[40] Overgroups of symplectic group in linear group over local rings
You, H
Zheng, BD
COMMUNICATIONS IN ALGEBRA, 2001, 29 (06) : 2313 - 2318

← 1 2 3 4 5 →