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摘要翻译：
在函数域算法中，Drinfeld模起着椭圆曲线在数域算法中所起的作用。作为Drinfeld模的高维推广和阿贝尔变体的适当类似，G.Anderson引入了纯T-动机。本文研究了后者的算法。我们研究了哪些纯T动机是半单的，即等同于简单T动机的直接和。我们给出了不是半单的纯T-动机的例子。在有限域上，半单性等价于自同态代数的半单性，但在无限域上，这种等价于自同态代数的半单性是失败的。在有限域上，我们还研究了纯T-动机的自同态环和同质性存在的判据。我们得到了类似于塔特对阿贝尔变种的著名结果的答案。
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英文标题：
《Pure Anderson Motives over Finite Fields》
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作者：
Matthias Bornhofen, Urs Hartl
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian varieties, G. Anderson introduced pure t-motives. In this article we study the arithmetic of the later. We investigate which pure t-motives are semisimple, that is, isogenous to direct sums of simple ones. We give examples for pure t-motives which are not semisimple. Over finite fields the semisimplicity is equivalent to the semisimplicity of the endomorphism algebra, but also this fails over infinite fields. Still over finite fields we study the endomorphism rings of pure t-motives and criteria for the existence of isogenies. We obtain answers which are similar to Tate's famous results for abelian varieties.
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PDF链接：
https://arxiv.org/pdf/0709.2815
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