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

[21] CYCLOTOMIC SCHEMES OVER FINITE, COMMUTATIVE, ADMISSIBLE RINGS
GOLDBACH, RW
CLAASEN, HL
INDAGATIONES MATHEMATICAE-NEW SERIES, 1992, 3 (03): : 277 - 299
[22] Association schemes of affine type over finite rings
Tanaka, H
ADVANCES IN GEOMETRY, 2004, 4 (02) : 241 - 261
[23] (STRONGLY) GORENSTEIN FLAT MODULES OVER GROUP RINGS
Bahlekeh, Abdolnaser
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 90 (01) : 57 - 64
[24] DIEUDONNE MODULES OF FINITE LOCAL GROUP SCHEMES
OORT, F
PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1974, 77 (03): : 284 - 292
[25] Local duality for representations of finite group schemes
Benson, Dave
Iyengar, Srikanth B.
Krause, Henning
Pevtsova, Julia
COMPOSITIO MATHEMATICA, 2019, 155 (02) : 424 - 453
[26] INVOLUTORY MATRICES OVER FINITE LOCAL RINGS
MCDONALD, BR
CANADIAN JOURNAL OF MATHEMATICS, 1972, 24 (03): : 369 - &
[27] DUADIC CODES OVER FINITE LOCAL RINGS
Karbaski, Arezoo Soufi
Samei, Karim
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 59 (02) : 265 - 276
[28] A NOTE ON INVARIANTS OVER FINITE LOCAL RINGS
Chen, Yin
COMMUNICATIONS IN ALGEBRA, 2013, 41 (09) : 3218 - 3223
[29] Symplectic graphs over finite local rings
Meemark, Yotsanan
Puirod, Thammanoon
EUROPEAN JOURNAL OF COMBINATORICS, 2013, 34 (07) : 1114 - 1124
[30] On *-clean group rings over finite fields
Han, Dongchun
Zhang, Hanbin
FINITE FIELDS AND THEIR APPLICATIONS, 2021, 73

← 1 2 3 4 5 →