p-adic Arakelov theory
p-adic Arakelov theory
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p进阿拉克洛夫理论
DOI：
10.1016/j.jnt.2004.11.010
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发表时间：
2003
影响因子：
0.7
通讯作者：
Amnon Besser
中科院分区：
文献类型：
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作者：
Amnon Besser
我们介绍算术曲面上的Arakelov交理论的p-adic模拟。在科尔曼和格罗斯所描述的0次因子的p-adic高度配对的扩展中的交叉配对。它还使用了科尔曼集成和相关的工作科尔梅兹对p-adic绿色功能。引入度量化线丛的p-adic形式，并以Faltings的形式定义了其上同调行列式的度量。我们还证明了伴随公式和Riemann-Roch公式的类似物。
We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work of Colmez on p-adic Green functions. We introduce the p-adic version of a metrized line bundle and define the metric on the determinant of its cohomology in the style of Faltings. We also prove analogues of the Adjunction formula and the Riemann–Roch formula.