FORMAL GROUPS AND CONGRUENCES FOR L-FUNCTIONS
FORMAL GROUPS AND CONGRUENCES FOR L-FUNCTIONS
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L 函数的形式群和同余式
DOI：
10.2307/2374587
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
J. Stienstra
中科院分区：
文献类型：
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作者：
J. Stienstra
导论.本文给出了定义在Z上的有限型平坦环上的一大类概型的同余，类似于Atkin和Swinnerton-Dyer [2，6]中的同余，其中包括任意维数和亏格的pN的分支双覆盖。第1-4节的结果合在一起得到下面的定理。定理0.1。设K是Z上平坦的有限型环。设R ∈ K[T0，. . * ，TN]是2d次的齐次多项式。假设2d > 2N > 0。设θ C是由方程U2 = R给出的PZ的双重覆盖（其中U是权重为d的新变量）。设（P）是K的极大理想，其剩余域K/1@的特征为p，阶为q = pf.设e是一个整数，使得I < e。p - 1和p e（我们。
Introduction. In this note we show congruences, similar to those of Atkin and Swinnerton-Dyer [2, 6], for a large class of schemes, including branched double coverings of pN of arbitrary dimension and genus, defined over any ring which is flat and of finite type over Z. The results of sections 1-4 together yield the following theorem. THEOREM 0.1. Let K be a ring which is flat and offinite type over Z. Let R E K[T0, . . *, TN] be a homogeneous polynomial of degree 2d. Assume 2d > 2N > 0. Let 9C be the double covering of PZ given by the equation U2 = R (where U is a new variable of weight d). Let (P be a maximal ideal of K with residue field K/1@ of characteristic p and of order q = p f. Let e be an integer such that I < e ? p - 1 and p e (We.