Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/oxford-university-press/the-manin-mumford-conjecture-a-brief-survey-t0wsUoWL23
References (72)
-
H. Grauert (1965)
Mordells Vermutung über rationale Punkte auf algebraischen Kurven und FunktionenkörperPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 25
-
M. Kurihara (1992)
Some remarks on conjectures about cyclotomic fields and $K$-groups of $\mathbf {Z}$Compositio Mathematica, 81
-
(1996)
Hauteurs et discrétude’, Séminaire Bourbaki, 49ème année -
Paul Vojta (1991)
Siegel's theorem in the compact caseAnnals of Mathematics, 133
-
G. Faltings (1983)
Endlichkeitssätze für abelsche Varietäten über ZahlkörpernInventiones mathematicae, 73
-
M. Laurent (1984)
Equations diophantiennes exponentiellesInventiones mathematicae, 78
-
R. Coleman (1989)
Torsion points on abelian étale coverings of ¹-{0,1,∞}Transactions of the American Mathematical Society, 311
-
(1996)
an explicit bound’, Compositio Math -
S. Lang (1965)
Division points on curvesAnnali di Matematica Pura ed Applicata, 70
-
(1997)
a survey’, Arithmetic geometry (Cortona 1994), Sympos -
David Rohrlich (1977)
Points at infinity on the Fermat curvesInventiones mathematicae, 39
-
J. Voloch (1991)
On the conjectures of Mordell and Lang in positive characteristicsInventiones mathematicae, 104
-
R. Coleman (1986)
Torsion points on fermat curvesCompositio Mathematica, 58
-
R. Coleman (1987)
Ramified torsion points on curvesDuke Mathematical Journal, 54
-
R. Coleman (1985)
Torsion points on curves and p-adic Abelian integralsAnnals of Mathematics, 121
-
P. Samuel (1966)
Compléments a un article de Hans Grauert sur la conjecture de MordellPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 29
-
(1983)
Complex multiplication, Grundlehren Math. Wiss -
A. Buium (1992)
Intersections in jet spaces and a conjecture of S. LangAnnals of Mathematics, 136
-
Course at theColì ege de France -
M. Hindry (1988)
Autour d'une conjecture de Serge LangInventiones mathematicae, 94
-
E. Hrushovski (1996)
The Mordell-Lang conjecture for function fieldsJournal of the American Mathematical Society, 9
-
L. Szpiro, E. Ullmo, Shousong Zhang (1997)
Equirépartition des petits pointsInventiones mathematicae, 127
-
C. Chai (1991)
A Note on Manin's Theorem of the KernelAmerican Journal of Mathematics, 113
-
E. Bombieri (1990)
The Mordell conjecture revisitedAnnali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 17
-
A. Buium (1994)
On a question of B. MazurDuke Mathematical Journal, 75
-
A. Pillay (1997)
Model theory and diophantine geometryBulletin of the American Mathematical Society, 34
-
R. Coleman, Akio Tamagawa, P. Tzermias (1998)
THE CUSPIDAL TORSION PACKET ON THE FERMAT CURVECrelle's Journal, 1998
-
B. Mazur, D. Goldfeld (1978)
Rational isogenies of prime degreeInventiones mathematicae, 44
-
D. Abramovich, J. Voloch (1992)
Toward a proof of the Mordell-Lang conjecture in characteristic pInternational Mathematics Research Notices, 1992
-
Y. Bilu (1997)
Limit distribution of small points on algebraic toriDuke Mathematical Journal, 89
-
(1974)
C. R. Acad. Sci. Paris -
R. Greenberg (1980)
On the jacobian variety of some algebraic curvesCompositio Mathematica, 42
-
M. Raynaud (1983)
Sous-variétés d’une variété abélienne et points de torsion -
Lang Serge (1991)
Number Theory III: Diophantine Geometry -
K. Ribet (1999)
Torsion points on J0(N) and Galois representations -
P. Cohn (1974)
INTRODUCTION TO ALGEBRAIC AND ABELIAN FUNCTIONSBulletin of The London Mathematical Society, 6
-
E. Hrushovski (2001)
The Manin-Mumford conjecture and the model theory of difference fieldsAnn. Pure Appl. Log., 112
-
J. Voloch (1997)
Torsion points on y^2=x^6+1arXiv: Number Theory
-
M. McQuillan (1995)
Division points on semi-abelian varietiesInventiones mathematicae, 120
-
Y. Manin (1996)
Rational points on algebraic curves over function elds -
John Boxall, David Grant (2000)
Examples of torsion points on genus two curvesTransactions of the American Mathematical Society, 352
-
M. Baker (2000)
Torsion points on modular curvesInventiones mathematicae, 140
-
Ju. Manin (1972)
PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVESMathematics of The Ussr-izvestiya, 6
-
B. Poonen (1998)
Mordell-Lang plus BogomolovInventiones mathematicae, 137
-
(1998)
Minorations des hauters normalisées des sous-variétés de variétés abéliennes -
G. Faltings (1986)
Finiteness Theorems for Abelian Varieties over Number Fields -
(1991)
Diophantine geometry, Encyclopaedia Math -
Antoine Chambert-Loir (1999)
Points de petite hauteur sur les variétés semi-abéliennesAnnales Scientifiques De L Ecole Normale Superieure, 33
-
Shou-wu Zhang (1995)
POSITIVE LINE BUNDLES ON ARITHMETIC VARIETIESJournal of the American Mathematical Society, 8
-
Fedor Bogomolov (1980)
Sur l'algebricite des representations l-adiques, 290
-
R. Doran, Ze-Li Dou, G. Gilbert (1999)
Automorphic Forms, Automorphic Representations, and Arithmetic -
B. Mazur (1977)
Modular curves and the eisenstein idealPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 47
-
The University of Arizona, Tucson 85721-0089, USA E-mail address: tzermias@math.arizona -
P. Colmez (1998)
Intégration sur les variétés p-adiques -
F. Bogomolov (1980)
Points of finite order on abelian varieties, 44
-
(1998)
Torsion points on the Jacobian of a hyperelliptic image of a Fermat curve -
V. Drinfel'd (1973)
Two theorems on modular curvesFunctional Analysis and Its Applications, 7
-
A. Pillay (1998)
Erratum to “Model Theory and Diophantine Geometry”Bulletin of the American Mathematical Society, 35
-
B. Poonen (2000)
Genus-two curves with 22 torsion pointsComptes Rendus De L Academie Des Sciences Serie I-mathematique, 330
-
Paul Vojta (1996)
Integral points on subvarieties of semiabelian varieties, IInventiones mathematicae, 126
-
Shou-wu Zhang (1998)
Equidistribution of small points on abelian varietiesAnnals of Mathematics, 147
-
B. Mazur, P. Swinnerton-Dyer (1974)
Arithmetic of Weil curvesInventiones mathematicae, 25
-
R. Coleman (1987)
Torsion Points on Curves -
A. Buium, J. Voloch (1996)
Lang’s conjecture in characteristic $p$ : an explicit boundCompositio Mathematica, 103
-
(1998)
Department of Mathematics P.O. Box 210089 617 N. Santa Rita The University of Arizona Tucson -
J. Cassels, E. Flynn (1996)
Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2: Weddle's surface -
A. Buium (1993)
Effective bound for the geometric Lang conjectureDuke Mathematical Journal, 71
-
E. Ullmo (1996)
Positivite et discretion des points algebriques des courbesAnnals of Mathematics, 147
-
M. Raynaud (1983)
Courbes sur une variété abélienne et points de torsionInventiones mathematicae, 71
-
Contemp. Math -
A. Buium (1996)
Geometry of $p$-jetsDuke Mathematical Journal, 82
-
B. Gross, David Rohrlich (1978)
Some results on the Mordell-Weil group of the Jacobian of the Fermat curveInventiones mathematicae, 44
- Publisher
- Oxford University Press
- Copyright
- © London Mathematical Society
- ISSN
- 0024-6093
- eISSN
- 1469-2120
- DOI
- 10.1112/S0024609300007578
- Publisher site
- See Article on Publisher Site
Abstract
Abstract The Manin–Mumford conjecture asserts that if K is a field of characteristic zero, C a smooth proper geometrically irreducible curve over K , and J the Jacobian of C , then for any embedding of C in J , the set C ( K )∩ J ( K ) tors is finite. Although the conjecture was proved by Raynaud in 1983, and several other proofs have appeared since, a number of natural questions remain open, notably concerning bounds on the size of the intersection and the complete determination of C ( K )∩ J ( K ) tors for special families of curves C . The first half of this survey paper presents the Manin–Mumford conjecture and related general results, while the second describes recent work mostly dealing with the above questions. 1991 Mathematics Subject Classification 11G10, 11G30, 11G35, 14G25, 14H25, 14H40. © London Mathematical Society
Journal
Bulletin of the London Mathematical Society – Oxford University Press
Published: Nov 1, 2000