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摘要翻译：
研究了有限域上定义的K3曲面的算法。特别地，我们证明了特征p>3的有限域k上的任何有限高的K3曲面对特征0具有拟正则提升，并且对于任何这种提升，作为Hodge模的超越圈的内同态代数是CM域。证明了某些两个K3曲面乘积的Tate猜想。我们举例说明了如何显式地确定K上K3曲面的形式Brauer群。这里讨论的例子都是超几何类型的。
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英文标题：
《K3 surfaces of finite height over finite fields》
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作者：
J.-D. Yu and N. Yui
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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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英文摘要：
Arithmetic of K3 surfaces defined over finite fields is investigated. In particular, we show that any K3 surface of finite height over a finite field k of characteristic p > 3 has a quasi-canonical lifting to characteristic 0, and that for any such lifting, the endormorphism algebra of the transcendental cycles, as a Hodge module, is a CM field. The Tate conjecture for the product of certain two K3 surfaces is also proved. We illustrate by examples how to determine explicitly the formal Brauer group associated to a K3 surface over k. Examples discussed here are all of hypergeometric type.
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PDF链接：
https://arxiv.org/pdf/0709.1979
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