On the essential dimension of cyclic p-groups

被引：26
|
作者：
Florence, Mathieu [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, FSB MA, CH-1015 Lausanne, Switzerland
来源：
INVENTIONES MATHEMATICAE | 2008年 / 171卷 / 01期
关键词：
Algebraic Group; Essential Dimension; Division Algebra; Linear Algebraic Group; Central Simple Algebra;
D O I：
10.1007/s00222-007-0079-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have ed(Q)(Z/8Z)=4, a result which was conjectured by Buhler and Reichstein in 1995 (unpublished). ii) We have ed(Q)(Z/p(r) Z) >= p(r-1).
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页码：175 / 189
页数：15
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