Arakelov geometry over an adelic curve
Lecture 1 Huayi CHEN
Course Description
In a series of lectures I will present a new framework of Arakelov geometry proposed by Atsushi Moriwaki and myself, namely Arakelov geometry over an adelic curve.
In our setting, an adelic curve refers to a field equipped with a family of absolute values (with possible repetitions) parametrised by a measure space. I will begin with an introduction on elementary geometry of numbers and Arakelov geometry of number fields and function fields and then explain why the setting of adelic curves is natural and permits to unify several frameworks in the literature which could be apparently transversal: Arakelov geometry over number fields and function fields, arithmetic geometry over a finitely generated field (Moriwaki), height theory of Mfields (Gubler), Rfiltration method (Chen), Siegel fields (Gaudron and Rémond). The construction of arithmetic objects and arithmetic invariants will be discussed, with an emphasis on the geometry of adelic vector bundles and its relationship with the classic geometry of numbers and Arakelov theory.
The lectures will be concluded by a view of further research topics and open problems.

 Lecture 1

Huayi CHEN
Oct. 30, 2018 1:36:58 English

 Lecture 2

Huayi CHEN
Oct. 30, 2018 1:31:19 English

 Lecture 3

Huayi CHEN
Oct. 30, 2018 1:31:31 English

 Lecture 4

Huayi CHEN
Oct. 30, 2018 1:34:35 English

 Lecture 5

Huayi CHEN
Oct. 30, 2018 1:24:35 English

 Lecture 6

Huayi CHEN
Oct. 30, 2018 1:29:57 English

 Lecture 7

Huayi CHEN
Oct. 30, 2018 1:38:25 English
Details
 Year/Term
 2018 / Intensive, Second semester
 Date
 October 2nd to October 30th, 2018
 Faculty/
Graduate School  Graduate School of Science
 Language
 English
 Instructor name
 Huayi CHEN（Distinguished Visiting Professor,Kyoto University / Professor, Université Paris Diderot）
 Place
 Room 110, Graduate School of Science Bldg No 3
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