摘要翻译:
设$F$为具有整数环的局部非阿基米德域$O$。设$\bfx$是$O$剩余域的代数闭包上$F$-height$N$的一维形式$O$-模。根据Drinfeld的工作,$\bfx$的泛变形$x$是在$n-1$变量的幂级数环$r_0$上的形式群,其最大未分枝扩张是$O$的完成。对于$h\in\{0,...,n-1\}$来说,让$u_h$是$\spec(R_0)$的子方案,其中$x$的关联可分模块的连通部分具有$h$的高度。利用Drinfeld能级结构理论,我们证明了在etale商的Tate模上,$u_h$的基本群的表示是满射的。
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英文标题:
《Galois actions on torsion points of universal one-dimensional formal
modules》
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作者:
Matthias Strauch
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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: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:
Let $F$ be a local non-Archimedean field with ring of integers $o$. Let $\bf X$ be a one-dimensional formal $o$-module of $F$-height $n$ over the algebraic closure of the residue field of $o$. By the work of Drinfeld, the universal deformation $X$ of $\bf X$ is a formal group over a power series ring $R_0$ in $n-1$ variables over the completion of the maximal unramified extension of $o$. For $h \in \{0,...,n-1\}$ let $U_h$ be the subscheme of $\Spec(R_0)$ where the connected part of the associated divisible module of $X$ has height $h$. Using the theory of Drinfeld level structures we show that the representation of the fundamental group of $U_h$ on the Tate module of the etale quotient is surjective.
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PDF链接:
https://arxiv.org/pdf/0709.3542