On $d$-gonality of Drinfel'd modular curves and strong Uniform Boundedness Conjecture
NguyenKhac, Viet ; Yamada, Shin-ichiro
Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, p. 126-129 / Harvested from Project Euclid
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We give an upper bound of the level $\mathfrak{n}$ by means of $d$-gonality of the Drinfel'd modular curves $X_0(\mathfrak{n})$ mod $\mathfrak{p}$ for $\mathfrak{p} \nmid \mathfrak{n}$. As a corollary of the result, we obtain an estimation in the strong Uniform Boundedness Conjecture for Drinfel'd modules of rank 2. We also discuss some asymptotically (and practically) good bound in this connection.
Publié le : 2001-09-14
Classification:  $d$-gonality,  Drinfel'd modular curve,  strong uniform boundedness conjecture,  bounding torsions,  11G09,  11G30,  14H10 
@article{1148393037,
     author = {NguyenKhac, Viet and Yamada, Shin-ichiro},
     title = {On $d$-gonality of Drinfel'd modular curves and strong Uniform Boundedness Conjecture},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {77},
     number = {10},
     year = {2001},
     pages = { 126-129},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393037}
}

NguyenKhac, Viet; Yamada, Shin-ichiro. On $d$-gonality of Drinfel'd modular curves and strong Uniform Boundedness Conjecture. Proc. Japan Acad. Ser. A Math. Sci., Tome 77 (2001) no. 10, pp.  126-129. http://gdmltest.u-ga.fr/item/1148393037/