On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves
On the torsion of the Mordell-Weil group of the Jacobian of Drinfeld modular curves
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德林菲尔德模曲线雅可比行列式的 Mordell-Weil 群的挠率
DOI：
10.4171/dm/185
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发表时间：
2005
影响因子：
0.9
通讯作者：
Ambrus Pál
中科院分区：
文献类型：
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作者：
Ambrus Pál
设Y_0（p）是F_q [T ]上秩为2的Drinfeld模的Drinfeld模曲线，其一般特征为具有Hecke水平p-结构，其中p ∈ F_q [T ]是d次素理想.设J_0（p）表示包含Y_0（p）的唯一光滑不可约射影曲线的雅可比矩阵。如果d是奇数，则定义N（p）= q−1 q−1，否则定义N（p）= q −1 q2−1。证明了交换簇J 0（p）的Fq（T）值点群的扭子群是尖点除子群，其阶为N（p）.类似地，交换簇J 0（p）的最大μ-型有限etale子群方案是Shimura群方案，阶为N（p）。通过对曲线Y_0（p）的Hecke代数T（p）的Eisenstein理想E（p）的研究得到了我们的结果。沿着这条路，我们证明了Hecke代数T（p）在E（p）的支撑下的任意极大理想上的完备化是Gorenstein. 2000年数学科目分类：小学11 G18;中学11 G 09。
Let Y0(p) be the Drinfeld modular curve parameterizing Drinfeld modules of rank two over Fq[T ] of general characteristic with Hecke level p-structure, where p ⊳ Fq[T ] is a prime ideal of degree d. Let J0(p) denote the Jacobian of the unique smooth irreducible projective curve containing Y0(p). Define N(p) = q−1 q−1 , if d is odd, and define N(p) = q −1 q2−1 , otherwise. We prove that the torsion subgroup of the group of Fq(T )-valued points of the abelian variety J0(p) is the cuspidal divisor group and has order N(p). Similarly the maximal μ-type finite etale subgroup-scheme of the abelian variety J0(p) is the Shimura group scheme and has order N(p). We reach our results through a study of the Eisenstein ideal E(p) of the Hecke algebra T(p) of the curve Y0(p). Along the way we prove that the completion of the Hecke algebra T(p) at any maximal ideal in the support of E(p) is Gorenstein. 2000 Mathematics Subject Classification: Primary 11G18; Secondary 11G09.