# Endlichkeitssätze für abelsche Varietäten über Zahlkörpern

@article{Faltings1983EndlichkeitsstzeFA,
title={Endlichkeitss{\"a}tze f{\"u}r abelsche Variet{\"a}ten {\"u}ber Zahlk{\"o}rpern},
author={Gerd Faltings},
journal={Inventiones mathematicae},
year={1983},
volume={73},
pages={349-366}
}
• G. Faltings
• Published 1983
• Mathematics
• Inventiones mathematicae
1,113 Citations
The Shafarevich conjecture for hypersurfaces in abelian varieties
• Mathematics
• 2020
Faltings proved that there are finitely many abelian varieties of genus $g$ of a number field $K$, with good reduction outside a finite set of primes $S$. Fixing one of these abelian varieties $A$,Expand
On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem
• Mathematics
• Michigan Mathematical Journal
• 2019
In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dependence in theExpand
Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture
• Mathematics
• 2016
In the first part we construct algorithms which we apply to solve S-unit, Mordell, cubic Thue, cubic Thue-Mahler and generalized Ramanujan-Nagell equations. As a byproduct we obtain alternativeExpand
Anabelian geometry and descent obstructions on moduli spaces
• Mathematics
• 2015
We study the section conjecture of anabelian geometry and the sufficiency of the finite descent obstruction to the Hasse principle for the moduli spaces of principally polarized abelian varieties andExpand
Deux problèmes de décompte diophantien
Nous traitons ici de questions d’effectivite dans les problemes de Mordell-Lang et de Schanuel ou la notion de hauteur algebrique joue un role central.Dans un premier temps nous revisitions laExpand
Good reduction of Fano threefolds and sextic surfaces
• Mathematics
• 2015
We investigate versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings, for other classes of varieties. We first obtain analogues for certain Fano threefolds.Expand
Height of motives
We define the height of a motive over a number field. We show that if we assume the finiteness of motives of bounded height, Tate conjecture for the $p$-adic Tate module can be proved for motivesExpand
On the modular curve X_0(23)
Abstract. The Jacobian J0(23) of the modular curve X0(23) is a semi-stable abelian variety over Q with good reduction outside 23. It is simple. We prove that every simple semi-stable abelian varietyExpand
Rational Points in Arithmetic Progressions on y 2 = xn + k
• M. Ulas
• Mathematics
• 2012
Abstract Let $C$ be a hyperelliptic curve given by the equation ${{y}^{2}}\,=\,f(x)$ for $f\,\in \,\mathbb{Z}[x]$ without multiple roots. We say that pointsExpand

#### References

SHOWING 1-10 OF 12 REFERENCES
Séminaire sur les pinceaux de courbes de genre au moins deux
• 1981
PENCILS OF CURVES OF GENUS AT LEAST TWO (a seminar at the E.N.S. organised by L. Szpiro) This seminar contains eigth papers that we can divided int o four groups : Semi-stable réduction (expos é 1 byExpand
A REMARK ON ENDOMORPHISMS OF ABELIAN VARIETIES OVER FUNCTION FIELDS OF FINITE CHARACTERISTIC
Assuming Tate's finiteness conjecture, we prove some consequences of Tate's conjecture on homomorphisms of abelian varieties.
INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
In this article it is explained how to construct for a nonsingular model of a curve defined over a number field a theory analogous to the theory of divisors, and the intersection numbers of divisors,Expand
ISOGENIES OF ABELIAN VARIETIES OVER FIELDS OF FINITE CHARACTERISTIC
It is proved that Tate's finiteness conjecture for isogenies of Abelian varieties over fields of characteristic other than 2 can be formally deduced from the conjecture on the resolution ofExpand
FAMILIES OF ALGEBRAIC CURVES WITH FIXED DEGENERACIES
In this paper we prove that there exist only finitely many nonisomorphic and nonconstant curves of fixed genus, defined over a fixed function field and having bad reductions at a given finite set ofExpand
The irreducibility of the space of curves of given genus
• Mathematics
• 1969
© Publications mathematiques de l’I.H.E.S., 1969, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.Expand
ALGEBRAIC CURVES OVER FUNCTION FIELDS. I
This paper studies the diophantine geometry of curves of genus greater than unity defined over a one-dimensional function field.