On the Tame Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic > 0
On the Tame Fundamental Groups of Curves over Algebraically Closed Fields of Characteristic > 0
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关于特征 > 0 代数闭域上的驯化基本曲线群
DOI：
10.1155/s1073792899000446
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发表时间：
1999
影响因子：
0.7
通讯作者：
Akio Tamagawa
中科院分区：
文献类型：
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作者：
Akio Tamagawa
证明了特征p > 0的代数闭域k上光滑连通曲线的驯服基本群的同构类决定了曲线的亏格g和穿孔数n，除非（g，n）=（0，0），（0，1）.此外，假设g = 0，n > 1，且k是素域Fp的代数闭包，我们证明了驯服基本群的同构类甚至完全决定了曲线的同构类作为一个概型（尽管不一定是k-概型）。作为证明这些结果的一个重要工具，我们推广了雷诺的θ因子理论。
We prove that the isomorphism class of the tame fundamental group of a smooth, connected curve over an algebraically closed eld k of characteristic p > 0 determines the genus g and the number n of punctures of the curve, unless (g, n) = (0, 0), (0, 1). Moreover, assuming g = 0, n > 1, and that k is the algebraic closure of the prime eld Fp, we prove that the isomorphism class of the tame fundamental group even completely determines the isomorphism class of the curve as a scheme (though not necessarily as a k-scheme). As a key tool to prove these results, we generalize Raynaud's theory of theta divisors.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
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作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest