EXPERIMENTS WITH CERESA CLASSES OF CYCLIC FERMAT QUOTIENTS

David T.B.G. Lilienfeldt; Ari Shnidman

doi:10.1090/proc/16178

EXPERIMENTS WITH CERESA CLASSES OF CYCLIC FERMAT QUOTIENTS

David T.B.G. Lilienfeldt, Ari Shnidman

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, the central value of the L-function of the relevant motive is non-vanishing and the Ceresa cycle is torsion in the Griffiths group, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients.

Original language	English
Pages (from-to)	931-947
Number of pages	17
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	3
DOIs	https://doi.org/10.1090/proc/16178
State	Published - 1 Mar 2023

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/proc/16178

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title = "EXPERIMENTS WITH CERESA CLASSES OF CYCLIC FERMAT QUOTIENTS",

abstract = "We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, the central value of the L-function of the relevant motive is non-vanishing and the Ceresa cycle is torsion in the Griffiths group, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients.",

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AB - We give two new examples of non-hyperelliptic curves whose Ceresa cycles have torsion images in the intermediate Jacobian. For one of them, the central value of the L-function of the relevant motive is non-vanishing and the Ceresa cycle is torsion in the Griffiths group, consistent with the conjectures of Beilinson and Bloch. We speculate on a possible explanation for the existence of these torsion Ceresa classes, based on some computations with cyclic Fermat quotients.

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JF - Proceedings of the American Mathematical Society

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EXPERIMENTS WITH CERESA CLASSES OF CYCLIC FERMAT QUOTIENTS

Abstract

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