l-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture
l-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture
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l-进代数单数群、共字符和 Mumford-Tate 猜想
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发表时间：
1998
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通讯作者：
R. Pink
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作者：
R. Pink
证明了数域上与一个动机相关联的-adic代数单值群是由Hodge数所决定的某些单参数子群生成的.在一个阿贝尔品种的特殊情况下，我们得到更强的声明说，大致`-adic代数单值群看起来像一个Mumford-Tate群的一些（其他？）阿贝尔簇当自同态环为Z且维数满足一定的数值条件时，我们导出了这一交换簇的Mumford-Tate猜想。我们还讨论了寻找普通约化的地方的问题。
We prove that the `-adic algebraic monodromy groups associated to a motive over a number field are generated by certain one-parameter subgroups determined by Hodge numbers. In the special case of an abelian variety we obtain stronger statements saying roughly that the `-adic algebraic monodromy groups look like a Mumford-Tate group of some (other?) abelian variety. When the endomorphism ring is Z and the dimension satisfies certain numerical conditions, we deduce the Mumford-Tate conjecture for this abelian variety. We also discuss the problem of finding places of ordinary reduction.