Geodesic
On trees covering chains or stars
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 207-215 
F. B. Pakovich. On trees covering chains or stars. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 207-215. http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a11/
@article{FPM_2007_13_6_a11,
     author = {F. B. Pakovich},
     title = {On trees covering chains or stars},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {207--215},
     year = {2007},
     volume = {13},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a11/}
}
TY  - JOUR
AU  - F. B. Pakovich
TI  - On trees covering chains or stars
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2007
SP  - 207
EP  - 215
VL  - 13
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a11/
LA  - ru
ID  - FPM_2007_13_6_a11
ER  - 
%0 Journal Article
%A F. B. Pakovich
%T On trees covering chains or stars
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2007
%P 207-215
%V 13
%N 6
%U http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a11/
%G ru
%F FPM_2007_13_6_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, in the context of the “dessins d'enfants” theory, we give a combinatorial criterion for a plane tree to cover a tree from the classes of “chains” or “stars.” We also discuss some applications of this result that are related to the arithmetical theory of torsion on curves.

[1] Pakovich F., “O derevyakh, dopuskayuschikh morfizmy na zvezdy ili tsepi”, Uspekhi mat. nauk, 55:3 (2000), 593–594 | MR | Zbl

[2] Flynn E. F., “The arithmetic of hyperelliptic curves”, Algorithms in Algebraic Geometry and Applications, Progress Math., 143, Birkhäuser, Boston, 1996, 165–175 | MR | Zbl

[3] L. Schneps, P. Lochak (eds.), Geometric Galois Actions, Vol. 1: Around Grothendieck's Esquisse d'un Programme, Vol. 2: The Inverse Galois Problem, Moduli Spaces and Mapping Class Groups, London Math. Soc. Lect. Note Ser., 242, 243, Cambridge Univ. Press, Cambridge, 1997 | MR

[4] Leprévost F., “Famille de courbes hyperelliptique de genre $g$ munies d'une classe de diviseurs rationnels d'ordre $2g^2+4g+1$”, Séminaire de théorie des nombres, Paris, France, 1991–1992, Progress Math., 116, Birkhäuser, Boston, 1994, 107–119 | MR | Zbl

[5] Mazur B., “Rational points on modular curves”, Modular Functions of One Variable. V, Lect. Notes Math., 601, Springer, Berlin, 1977, 107–148 | MR

[6] Merel L., “Bornes pour la torsion des courbes elliptiques sur les corps de nombres”, Invent. Math., 124:1–3 (1996), 437–449 | DOI | MR | Zbl

[7] Pakovitch F., “Combinatoire des arbres planaires et arithmétique des courbes hyperelliptiques”, Ann. Inst. Fourier, 48:2 (1998), 1001–1029 | MR

[8] L. Schneps (ed.), The Grothendieck Theory of Dessins D'enfants, London Math. Soc. Lect. Note Ser., 200, Cambridge Univ. Press, Cambridge, 1994 | MR