An overview on problems of unlikely intersections in families of abelian varieties

Elliptic curves over global fields (11G05) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Global ground fields in algebraic geometry (14G25) Model theory (number-theoretic aspects) (11U09)

Cites Work

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On the Manin-Mumford and Mordell-Lang conjectures in positive characteristic
On the torsion anomalous conjecture in CM abelian varieties
Torsion points on families of squares of elliptic curves
Impossible intersections in a Weierstrass family of elliptic curves
Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
Diophantine approximation on abelian varieties
Algebraic curves and multiplicative equations.
Rational points in periodic analytic sets and the Manin-Mumford conjecture
A note on Maurin's theorem
Courbes sur une variété abélienne et points de torsion
Finiteness theorems for abelian varieties over number fields.
Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
Cohomological realization of a family of 1-motives
Deficient points on extensions of abelian varieties by \(G_ m\)
Siegel's theorem in the compact case
Torsion hypersurfaces on abelian schemes and Betti coordinates
A variant of a theorem by Ailon-Rudnick for elliptic curves
Division points on semi-abelian varieties
Unlikely intersections for curves in products of Carlitz modules
Uniformity in Mordell-Lang for curves
A mod \(p\) variant of the André-Oort conjecture
Pink's conjecture on unlikely intersections and families of semi-abelian varieties
On torsion anomalous intersections
Torsion points on families of products of elliptic curves
The rational points of a definable set
Division points on curves
Generalized greatest common divisors, divisibility sequences, and Vojta's conjecture for blowups
Torsion points, Pell's equation, and integration in elementary terms
Unlikely intersections of curves with algebraic subgroups in semiabelian varieties
Rational points on Grassmannians and unlikely intersections in tori
Special points on fibered powers of elliptic surfaces
Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
UNLIKELY INTERSECTIONS FOR CURVES IN MULTIPLICATIVE GROUPS OVER POSITIVE CHARACTERISTIC
O-minimality and certain atypical intersections
Relative Manin–Mumford for Semi-Abelian Surfaces
EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
A positive characteristic Manin–Mumford theorem
Division points on subvarieties of isotrivial semi-abelian varieties
On unlikely intersections of complex varieties with tori
On the Bounded Height Conjecture
Unlikely intersections in products of families of elliptic curves and the multiplicative group
Simultaneous Torsion in the Legendre Family
Multiplicative and Linear Dependence in Finite Fields and on Elliptic Curves Modulo Primes
Point-Counting and the Zilber–Pink Conjecture
On the Zilber-Pink conjecture for complex abelian varieties
Unlikely intersections in families of abelian varieties and the polynomial Pell equation
CM RELATIONS IN FIBERED POWERS OF ELLIPTIC FAMILIES
On the explicit Torsion Anomalous Conjecture
Anomalous Subvarieties—Structure Theorems and Applications
Exponential diophantine equations
Linear relations in families of powers of elliptic curves

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