Towards a dynamical manin-mumford conjecture

Dragos Ghioca; Thomas J. Tucker; Shouwu Zhang

doi:10.1093/imrn/rnq283

Towards a dynamical manin-mumford conjecture

Dragos Ghioca, Thomas J. Tucker, Shouwu Zhang

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

36 Scopus citations

Abstract

We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of ℙ¹ × ℙ¹.

Original language	English (US)
Pages (from-to)	5109-5122
Number of pages	14
Journal	International Mathematics Research Notices
Volume	2011
Issue number	22
DOIs	https://doi.org/10.1093/imrn/rnq283
State	Published - 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnq283

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title = "Towards a dynamical manin-mumford conjecture",

abstract = "We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of ℙ1 × ℙ1.",

author = "Dragos Ghioca and Tucker, \{Thomas J.\} and Shouwu Zhang",

note = "Funding Information: This work was partially supported by NSERC (to D.G.) and by NSF Grants 0801072 and 0854839",

year = "2011",

doi = "10.1093/imrn/rnq283",

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AU - Tucker, Thomas J.

AU - Zhang, Shouwu

N1 - Funding Information: This work was partially supported by NSERC (to D.G.) and by NSF Grants 0801072 and 0854839

PY - 2011

Y1 - 2011

N2 - We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of ℙ1 × ℙ1.

AB - We provide a family of counterexamples to a first formulation of the dynamical Manin-Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of ℙ1 × ℙ1.

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DO - 10.1093/imrn/rnq283

M3 - Article

AN - SCOPUS:81255134878

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EP - 5122

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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Towards a dynamical manin-mumford conjecture

Abstract

All Science Journal Classification (ASJC) codes

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