Eigenvalues of Frobenius and Hodge Numbers
Eigenvalues of Frobenius and Hodge Numbers
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Frobenius 和 Hodge 数的特征值
DOI：
10.4310/pamq.2006.v2.n2.a5
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发表时间：
2006
影响因子：
0.7
通讯作者：
G. Lehrer
中科院分区：
文献类型：
--
作者：
M. Kisin;G. Lehrer
研究了不同特征域上代数簇上同调的霍奇纯性之间的关系。具体地说，我们研究数域上的簇，它的上同调在某个固定的2i度完全由Hodge类组成，即它的Hodge上同调在2i度完全是（i，i）型。除此之外，我们给出了数域上的簇在有限域上的有理点满足这一性质的充分条件。
We study the connection between Hodge purity of the cohomology of algebraic varieties over fields of different characteristics. Specifically, we study varieties over number fields, whose cohomology in some fixed degree 2i consists entirely of Hodge classes, that is, whose Hodge cohomology in degree 2i is entirely of type (i, i). Among other things, we give sufficient conditions for varieties over number fields to satisfy this property in terms of their rational points over finite fields.