Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

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Standard

Unlikely intersections of curves with algebraic subgroups in semiabelian varieties. / Barroero, Fabrizio; Kühne, Lars; Schmidt, Harry.

I: Selecta Mathematica, New Series, Bind 29, Nr. 2, 18, 2023.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Barroero, F, Kühne, L & Schmidt, H 2023, 'Unlikely intersections of curves with algebraic subgroups in semiabelian varieties', Selecta Mathematica, New Series, bind 29, nr. 2, 18. https://doi.org/10.1007/s00029-022-00823-w

APA

Barroero, F., Kühne, L., & Schmidt, H. (2023). Unlikely intersections of curves with algebraic subgroups in semiabelian varieties. Selecta Mathematica, New Series, 29(2), [18]. https://doi.org/10.1007/s00029-022-00823-w

Vancouver

Barroero F, Kühne L, Schmidt H. Unlikely intersections of curves with algebraic subgroups in semiabelian varieties. Selecta Mathematica, New Series. 2023;29(2). 18. https://doi.org/10.1007/s00029-022-00823-w

Author

Barroero, Fabrizio ; Kühne, Lars ; Schmidt, Harry. / Unlikely intersections of curves with algebraic subgroups in semiabelian varieties. I: Selecta Mathematica, New Series. 2023 ; Bind 29, Nr. 2.

Bibtex

@article{f665de14982b4790a23079ab30f86cf8,
title = "Unlikely intersections of curves with algebraic subgroups in semiabelian varieties",
abstract = "Let G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over Q¯. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.",
keywords = "Heights, Semiabelian varieties, Unlikely intersections, Zilber–Pink conjecture",
author = "Fabrizio Barroero and Lars K{\"u}hne and Harry Schmidt",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",
year = "2023",
doi = "10.1007/s00029-022-00823-w",
language = "English",
volume = "29",
journal = "Selecta Mathematica, New Series",
issn = "1022-1824",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Unlikely intersections of curves with algebraic subgroups in semiabelian varieties

AU - Barroero, Fabrizio

AU - Kühne, Lars

AU - Schmidt, Harry

N1 - Publisher Copyright: © 2023, The Author(s).

PY - 2023

Y1 - 2023

N2 - Let G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over Q¯. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.

AB - Let G be a semiabelian variety and C a curve in G that is not contained in a proper algebraic subgroup of G. In this situation, conjectures of Pink and Zilber imply that there are at most finitely many points contained in the so-called unlikely intersections of C with subgroups of codimension at least 2. In this note, we establish this assertion for general semiabelian varieties over Q¯. This extends results of Maurin and Bombieri, Habegger, Masser, and Zannier in the toric case as well as Habegger and Pila in the abelian case.

KW - Heights

KW - Semiabelian varieties

KW - Unlikely intersections

KW - Zilber–Pink conjecture

U2 - 10.1007/s00029-022-00823-w

DO - 10.1007/s00029-022-00823-w

M3 - Journal article

AN - SCOPUS:85146660516

VL - 29

JO - Selecta Mathematica, New Series

JF - Selecta Mathematica, New Series

SN - 1022-1824

IS - 2

M1 - 18

ER -

ID: 382691408