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THE MORDELL–LANG CONJECTURE FOR SEMIABELIAN VARIETIES DEFINED OVER FIELDS OF POSITIVE CHARACTERISTIC

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  08 September 2023

DRAGOS GHIOCA Open the ORCID record for DRAGOS GHIOCA [Opens in a new window]  and
SHE YANG Open the ORCID record for SHE YANG [Opens in a new window]
DRAGOS GHIOCA*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver V6T 1Z2, Canada
SHE YANG
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing 100871, PR China e-mail: ys-yx@pku.edu.cn
*
e-mail: dghioca@math.ubc.ca
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Abstract

Let G be a semiabelian variety defined over an algebraically closed field K of prime characteristic. We describe the intersection of a subvariety X of G with a finitely generated subgroup of $G(K)$.

Keywords

semiabelian varietiesfinite fieldsMordell–Lang conjecture

MSC classification

Primary: 11G10: Abelian varieties of dimension $> 1$
Secondary: 14G17: Positive characteristic ground fields

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 2 , April 2024 , pp. 254 - 264
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is supported by a Discovery NSERC grant, while the second author is supported by an NSFC Grant (No. 12271007).

References

Faltings, G., ‘The general case of S. Lang’s conjecture’, in: Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspectives in Mathematics, 15 (eds. Cristante, V. and Messing, W.) (Academic Press, San Diego, CA, 1994), 175–182.CrossRefGoogle Scholar
Ghioca, D., ‘The isotrivial case in the Mordell–Lang theorem’, Trans. Amer. Math. Soc. 360(7) (2008), 3839–3856.CrossRefGoogle Scholar
Hrushovski, E., ‘The Mordell–Lang conjecture for function fields’, J. Amer. Math. Soc. 9(3) (1996), 667–690.CrossRefGoogle Scholar
Laurent, M., ‘Équations diophantiennes exponentielles’, Invent. Math. 78 (1984), 299–327.CrossRefGoogle Scholar
Moosa, R. and Scanlon, T., ‘The Mordell–Lang conjecture in positive characteristic revisited’, in: Model Theory and Applications, Quad. Mat., 11 (eds. L. Bélair, P. D'Aquino, D. Marker, M. Otero, F. Point and A. Wilkie) (Aracne, Rome, 2002), 273–296.Google Scholar
Moosa, R. and Scanlon, T., ‘F-structures and integral points on semiabelian varieties over finite fields’, Amer. J. Math. 126 (2004), 473–522.CrossRefGoogle Scholar
Vojta, P., ‘Integral points on subvarieties of semiabelian varieties. I’, Invent. Math. 126(1) (1996), 133–181.CrossRefGoogle Scholar