摘要翻译:
本文给出了给定迹和范数的有限域中元素个数的Katz界的一个改进。将该问题简化为一类toric Calabi-Yau超曲面上有理点数的估计,然后利用Rojas-Leon和第二作者对此类toric超曲面进行详细的上同调计算,得到了改进。
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英文标题:
《On Katz's bound for number of elements with given trace and norm》
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作者:
Marko Moisio, Daqing Wan
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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 this note an improvement of the Katz's bound on the number of elements in a finite field with given trace and norm is given. The improvement is obtained by reducing the problem to estimating the number of rational points on certain toric Calabi-Yau hypersurface, and then to use detailed cohomological calculations by Rojas-Leon and the second author for such toric hypersurfaces.
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PDF链接:
https://arxiv.org/pdf/0802.3200