Group schemes with strict O-action
Group schemes with strict O-action
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具有严格 O 行动的团体计划
DOI：
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发表时间：
2002
期刊：
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通讯作者：
G. Faltings
中科院分区：
文献类型：
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作者：
G. Faltings
设0表示p进局部域中的整数环。回想一下，o模是具有o作用的形式群，使得李代数上的诱导作用是通过标量的。本文将这一概念推广到有限平面群方案中。结果表明，通常的性质可以保留下来。例如，Cartier对偶性在用Lubin-Tate群代替乘法群时成立。我们还证明了在o分幂上的提升是由dieudonn<e:1>模控制的，或者更好地说是由复形控制的。对于这些事实，必须发明新的证明，因为经典的嵌入阿贝尔变体的方法
Let O denote the ring of integers in a p-adic local field. Recall that O-modules are formal groups with an O-action such that the induced action on the Lie algebra is via scalars. In the paper this notion is generalised to finite flat group schemes. It is shown that the usual properties carry over. For example, Cartier duality holds with the multiplicative group replaced by the Lubin–Tate group. We also show that liftings over O-divided powers are controlled by Dieudonné modules or, better, by complexes. For these facts new proofs have to be invented, because the classical recipe of embedding into abelian varieties