摘要翻译:
如果定义在局部域$k$上的具有有限剩余域$k$的射影光滑簇的$\ell$-adic上同调在余维$\ge1$上是支持的,则$k$整数环上的每个模型都有一个$k$-rational点。对于$K$a$P$-ADIC字段,这是Math/0405318,定理1.1。如果模型$\sx$是正则的,那么对于$k$-有理点数0704.1273有一个同余$\sx(k)\equiv1$模$k$,定理1.1。如果一个人放弃了正则性假设,那么同余性就被违反了。
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英文标题:
《Congruence for rational points over finite fields and coniveau over
local fields》
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作者:
H\'el\`ene Esnault and Chenyang Xu
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最新提交年份:
2007
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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:
If the $\ell$-adic cohomology of a projective smooth variety, defined over a local field $K$ with finite residue field $k$, is supported in codimension $\ge 1$, then every model over the ring of integers of $K$ has a $k$-rational point. For $K$ a $p$-adic field, this is math/0405318, Theorem 1.1. If the model $\sX$ is regular, one has a congruence $|\sX(k)|\equiv 1 $ modulo $|k|$ for the number of $k$-rational points 0704.1273, Theorem 1.1. The congruence is violated if one drops the regularity assumption.
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PDF链接:
https://arxiv.org/pdf/0706.0972