Available in electronic format
Available in print format
Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

The isotrivial case in the Mordell-Lang Theorem

Author(s): Dragos Ghioca
Journal: Trans. Amer. Math. Soc. 360 (2008), 3839-3856.
MSC (2000): Primary 11G10; Secondary 11G25
Posted: February 27, 2008
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $ G$ defined over a finite field with a closed subvariety $ X\subset G$. We also study a related question in the context of a power of the additive group scheme.


References:

1.
D. Abramovich and J. F. Voloch, Toward a proof of the Mordell-Lang conjecture in characteristic $ p$. Internat. Math. Res. Notices 5 (1992), 103-115. MR 1162230 (94f:11051)

2.
G. Faltings, The general case of S. Lang's conjecture. Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), 175-182, Perspect. Math., 15, Academic Press, San Diego, CA, 1994.

3.
D. Ghioca, The Mordell-Lang Theorem for Drinfeld modules. Internat. Math. Res. Notices, 53 (2005), 3273-3307. MR 2196099 (2006k:11105)

4.
D. Ghioca and R. Moosa, Division points on subvarieties of isotrivial semiabelian varieties, Internat. Math. Res. Notices 19 (2006), 1-23. MR 2264715 (2008c:14058)

5.
E. Hrushovski, The Mordell-Lang conjecture for function fields. J.Amer.Math.Soc 9 (1996), no.3, 667-690. MR 1333294 (97h:11154)

6.
M. Laurent, Equations diophantiennes exponentielles. Inventiones Math. 78 (1984), 299-327. MR 767195 (86j:11062)

7.
J. Milne, Abelian varieties. course notes available online at http://www.jmilne.org/math/.

8.
R. Moosa and T. Scanlon, F-structures and integral points on semiabelian varieties over finite fields. Amer. Journal of Math. 126 (2004), 473-522. MR 2058382 (2006f:11071)

9.
R. Moosa and T. Scanlon, The Mordell-Lang Conjecture in positive characteristic revisited. Model Theory and Applications (eds. L. Bélair, P. D'Aquino, D. Marker, M. Otero, F. Point, & A. Wilkie), 2003, 273-296. MR 2159720 (2007a:11085)

10.
B. Poonen, Local height functions and the Mordell-Weil theorem for Drinfeld modules, Compositio Math. 97 (1995), 349-368. MR 1353279 (96k:11075)

11.
J.-P. Serre, Lectures on the Mordell-Weil theorem. Translated from the French and edited by Martin Brown from notes by Michel Waldschmidt. Aspects of Mathematics, E15. Friedr. Vieweg & Sohn, Braunschweig, 1989. x+218 pp. MR 1002324 (90e:11086)


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11G10, 11G25

Retrieve articles in all Journals with MSC (2000): 11G10, 11G25


Additional Information:

Dragos Ghioca
Affiliation: Department of Mathematics & Statistics, Hamilton Hall, Room 218, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1
Address at time of publication: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada T1K 3M4
Email: dghioca@math.mcmaster.ca

DOI: 10.1090/S0002-9947-08-04388-2
PII: S 0002-9947(08)04388-2
Received by editor(s): February 7, 2006
Received by editor(s) in revised form: July 16, 2006
Posted: February 27, 2008
Copyright of article: Copyright 2008, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google