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
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References

SHOWING 1-10 OF 12 REFERENCES
Séminaire sur les pinceaux de courbes de genre au moins deux
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
© 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.
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