p-adic Arakelov theory

被引：14

作者：

Besser, A ^{[1
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

来源：

JOURNAL OF NUMBER THEORY | 2005年 / 111卷 / 02期

关键词：

Arakelov theory; p-adic height pairings; p-adic integration; p-adic Green functions;

D O I：

10.1016/j.jnt.2004.11.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：318 / 371

页数：54

共 19 条

[1]

Arakelov S. Ju., 1974, Izv. Akad. Nauk SSSR Ser. Mat., V38, P1179

[2]

Besser A, 2004, CRM PROC & LECT NOTE, V36, P13

[3] Coleman integration using the Tannakian formalism [J].