Albanese quotients of Picard modular surfaces, and rational points

来源 :Sino-French Conference on Arithmetic Geometry(中法算术几何会议) | 被引量 : 0次 | 上传用户：zhangyongqiangis250

【摘要】

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　　This is a report on a work in progress in collaboration with Dinakar Ramakrishnan.A celebrated result of Mazur proves that modular curves of large enough le

【作者】

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Dimitrov Mladen

【机构】

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UniversitédeLilleI

【出处】

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Sino-French Conference on Arithmetic Geometry(中法算术几何会议)

【发表日期】

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2013年6期

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　　This is a report on a work in progress in collaboration with Dinakar Ramakrishnan.A celebrated result of Mazur proves that modular curves of large enough level do not have rational points outside the cusps.Our aim is to establish a weak analogue for the Picard modular surfaces,which are Shimura varieties for a unitary group in three variables defined over an imaginary quadratic field.We prove that in many cases the Albanese variety has a quotient with a finite Mordell-Weil group and investigate consequences for the arithmetic of the Picard modular surface.

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Albanese quotients of Picard modular surfaces, and rational points

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