MOTIVES OVER FINITE FIELDS
MOTIVES OVER FINITE FIELDS
复制标题
有限领域的动机
DOI：
10.1090/pspum/055.1/1265538
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发表时间：
1994
影响因子：
1
通讯作者：
J. Milne
中科院分区：
文献类型：
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作者：
J. Milne
已知有限领域代数关闭的动机类别是半圣经的tannakian类别，但是除非有人假设泰特猜想，否则几乎没有人可以说。但是，一旦假定了这种猜想，就可以与其标准纤维函数一起对类别进行几乎完全令人满意的描述。特别是，可以列出将其表征为等价性的类别的属性，并证明（不假设任何猜想）确实存在具有这些属性的类别。 Hodge的猜想意味着，QAL上的CM-动物类别有一个函数，而F到F上的动机类别。我们构建了这样的函子。
The category of motives over the algebraic closure of a finite field is known to be a semisimple Q-linear Tannakian category, but unless one assumes the Tate conjecture there is little further one can say about it. However, once this conjecture is assumed, it is possible to give an almost entirely satisfactory description of the category together with its standard fibre functors. In particular it is possible to list properties of the category that characterize it up to equivalence and to prove (without assuming any conjectures) that there does exist a category with these properties. The Hodge conjecture implies that there is a functor from the category of CM-motives over Qal to the category of motives over F. We construct such a functor.