Adelic geometry on arithmetic surfaces II: Completed adeles and idelic Arakelov intersection theory

JOURNAL OF NUMBER THEORY

卷:211

Article

Czerniawska, Weronika¹  Dolce, Paolo² 

[1] Univ Geneva, Geneva, Switzerland

[2] Univ Udine, Udine, Italy

关键词: Adeles;    Local fields;    Global fields;    Arakelov geometry;    Arithmetic surfaces;    Intersection theory;    Number fields;   

DOI  :  10.1016/j.jnt.2019.10.010

来源: Elsevier

【 摘 要 】

We work with completed adelic structures on an arithmetic surface and justify that the construction under consideration is compatible with Arakelov geometry. The ring of completed adeles is algebraically and topologically self-dual and fundamental adelic subspaces are self orthogonal with respect to a natural differential pairing. We show that the Arakelov intersection pairing can be lifted to an idelic intersection pairing. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free