The intersection of a curve with algebraic subgroups in a product of elliptic curves
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)
- Volume: 2, Issue: 1, page 47-75
- ISSN: 0391-173X
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topViada, Evelina. "The intersection of a curve with algebraic subgroups in a product of elliptic curves." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.1 (2003): 47-75. <http://eudml.org/doc/84499>.
@article{Viada2003,
abstract = {We consider an irreducible curve $\{\mathcal \{C\}\}$ in $E^n$, where $E$ is an elliptic curve and $\{\mathcal \{C\}\}$ and $E$ are both defined over $\overline\{\mathbb \{Q\}\}$. Assuming that $\{\mathcal \{C\}\}$ is not contained in any translate of a proper algebraic subgroup of $E^n$, we show that the points of the union $\bigcup \{\mathcal \{C\}\} \cap A(\overline\{\mathbb \{Q\}\})$, where $A$ ranges over all proper algebraic subgroups of $E^n$, form a set of bounded canonical height. Furthermore, if $E$ has Complex Multiplication then the set $\bigcup \{\mathcal \{C\}\}\cap A(\overline\{\mathbb \{Q\}\})$, for $A$ ranging over all algebraic subgroups of $E^n$ of codimension at least $2$, is finite. If $E$ has no Complex Multiplication then the set $\bigcup \{\mathcal \{C\}\} \cap A(\overline\{\mathbb \{Q\}\})$ for $A$ ranging over all proper algebraic subgroups of $E^n$ of codimension at least $\frac\{n\}\{2\}+2$, is finite.},
author = {Viada, Evelina},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {47-75},
publisher = {Scuola normale superiore},
title = {The intersection of a curve with algebraic subgroups in a product of elliptic curves},
url = {http://eudml.org/doc/84499},
volume = {2},
year = {2003},
}
TY - JOUR
AU - Viada, Evelina
TI - The intersection of a curve with algebraic subgroups in a product of elliptic curves
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2003
PB - Scuola normale superiore
VL - 2
IS - 1
SP - 47
EP - 75
AB - We consider an irreducible curve ${\mathcal {C}}$ in $E^n$, where $E$ is an elliptic curve and ${\mathcal {C}}$ and $E$ are both defined over $\overline{\mathbb {Q}}$. Assuming that ${\mathcal {C}}$ is not contained in any translate of a proper algebraic subgroup of $E^n$, we show that the points of the union $\bigcup {\mathcal {C}} \cap A(\overline{\mathbb {Q}})$, where $A$ ranges over all proper algebraic subgroups of $E^n$, form a set of bounded canonical height. Furthermore, if $E$ has Complex Multiplication then the set $\bigcup {\mathcal {C}}\cap A(\overline{\mathbb {Q}})$, for $A$ ranging over all algebraic subgroups of $E^n$ of codimension at least $2$, is finite. If $E$ has no Complex Multiplication then the set $\bigcup {\mathcal {C}} \cap A(\overline{\mathbb {Q}})$ for $A$ ranging over all proper algebraic subgroups of $E^n$ of codimension at least $\frac{n}{2}+2$, is finite.
LA - eng
UR - http://eudml.org/doc/84499
ER -
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Citations in EuDML Documents
top- Evelina Viada, The optimality of the Bounded Height Conjecture
- Philipp Habegger, A Bogomolov property for curves modulo algebraic subgroups
- Nicolas Ratazzi, Borne sur la torsion dans les variétés abéliennes de type CM
- Nicolas Ratazzi, Intersection de courbes et de sous-groupes et problèmes de minoration de hauteur dans les variétés abéliennes C.M.
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