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

Weronika Czerniawska; Paolo Dolce

doi:10.1016/j.jnt.2019.10.010

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

Weronika Czerniawska, Paolo Dolce

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	235-296
Number of pages	62
Journal	Journal of Number Theory
Volume	211
DOIs	https://doi.org/10.1016/j.jnt.2019.10.010
State	Published - 1 Jun 2020
Externally published	Yes

Keywords

Adeles
Arakelov geometry
Arithmetic surfaces
Global fields
Intersection theory
Local fields
Number fields

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2019.10.010

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title = "Adelic geometry on arithmetic surfaces II: Completed adeles and idelic Arakelov intersection theory",

abstract = "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.",

keywords = "Adeles, Arakelov geometry, Arithmetic surfaces, Global fields, Intersection theory, Local fields, Number fields",

author = "Weronika Czerniawska and Paolo Dolce",

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AU - Dolce, Paolo

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Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - Adeles

KW - Arakelov geometry

KW - Arithmetic surfaces

KW - Global fields

KW - Intersection theory

KW - Local fields

KW - Number fields

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JO - Journal of Number Theory

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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