Arithmetic of Shimura curves

Shou Wu Zhang

doi:10.1007/s11425-010-0046-2

Arithmetic of Shimura curves

Shou Wu Zhang

Research output: Contribution to journal › Review article › peer-review

8 Scopus citations

Abstract

This is the note for a series of lectures that the author gave at the Centre de Recerca Matemática (CRM), Bellaterra, Barcelona, Spain on October 19-24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.

Original language	English (US)
Pages (from-to)	573-592
Number of pages	20
Journal	Science China Mathematics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1007/s11425-010-0046-2
State	Published - 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

CM-points
L-series
Shimura curves

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10.1007/s11425-010-0046-2

Cite this

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title = "Arithmetic of Shimura curves",

abstract = "This is the note for a series of lectures that the author gave at the Centre de Recerca Matem{\'a}tica (CRM), Bellaterra, Barcelona, Spain on October 19-24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.",

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year = "2010",

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PY - 2010

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N2 - This is the note for a series of lectures that the author gave at the Centre de Recerca Matemática (CRM), Bellaterra, Barcelona, Spain on October 19-24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.

AB - This is the note for a series of lectures that the author gave at the Centre de Recerca Matemática (CRM), Bellaterra, Barcelona, Spain on October 19-24, 2009. The aim is to give a comprehensive description of some recent work of the author and his students on generalisations of the Gross-Zagier formula, Euler systems on Shimura curves, and rational points on elliptic curves.

KW - CM-points

KW - L-series

KW - Shimura curves

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U2 - 10.1007/s11425-010-0046-2

DO - 10.1007/s11425-010-0046-2

M3 - Review article

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SP - 573

EP - 592

JO - Science China Mathematics

JF - Science China Mathematics

IS - 3

ER -

Arithmetic of Shimura curves

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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