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摘要翻译：
正如Deligne(2000)所说，在证明霍奇和泰特猜想的绝望中，我们可以试图找到替代品。对于特征零点上的阿贝尔变体，Deligne(1982)构造了一个Hodge类理论，它具有许多性质，如果Hodge猜想已知，代数类就会具有这些性质。在这篇文章中，我研究了是否存在一个关于有限域上的变体的“有理Tate类”理论，它具有如果Hodge和Tate猜想已知的话代数类所具有的性质。v3.提交的版本。
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英文标题：
《Rational Tate classes》
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作者：
J.S. Milne
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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：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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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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英文摘要：
In despair, as Deligne (2000) put it, of proving the Hodge and Tate conjectures, we can try to find substitutes. For abelian varieties in characteristic zero, Deligne (1982) constructed a theory of Hodge classes having many of the properties that the algebraic classes would have if the Hodge conjecture were known. In this article I investigate whether there exists a theory of "rational Tate classes" on varieties over finite fields having the properties that the algebraic classes would have if the Hodge and Tate conjectures were known. v3. Submitted version.
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PDF链接：
https://arxiv.org/pdf/0707.3167
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