A Survey of the Hodge-Arakelov Theory of Elliptic Curves II
A Survey of the Hodge-Arakelov Theory of Elliptic Curves II
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椭圆曲线Hodge-Arakelov理论综述II
DOI：
10.2969/aspm/03610081
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
S. Mochizuki
中科院分区：
文献类型：
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作者：
S. Mochizuki
本手稿的目的是给一个调查的Hodge-Arakelov理论的椭圆曲线（参见。[Mzk1，2]）-即，一种类似于经典复和p-adic霍奇理论的“椭圆曲线霍奇理论”，但它存在于Arakelov理论的全局算术框架中-因为这个理论存在于1999年10月在美国伯克利数学科学研究所（MSRI）举行的“伽罗瓦作用和几何”研讨会上。从那时起，各种进一步的重要发展发生在这个理论（参见。[Mzk3，4，5]等），但我们将不在本稿中详细讨论这些发展。
The purpose of the present manuscript is to give a survey of the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1,2]) — i.e., a sort of “Hodge theory of elliptic curves” analogous to the classical complex and p-adic Hodge theories, but which exists in the global arithmetic framework of Arakelov theory — as this theory existed at the time of the workshop on “Galois Actions and Geometry” held at the Mathematical Sciences Research Institute (MSRI) at Berkeley, USA, in October 1999. Since then, various further important developments have occurred in this theory (cf. [Mzk3,4,5], etc.), but we shall not discuss these developments in detail in the present manuscript.