Normalized period matrices II
Normalized period matrices II
复制标题
DOI：
10.2307/1970905
复制
发表时间：
1973-07
影响因子：
4.9
通讯作者：
B. Dwork
中科院分区：
文献类型：
--
作者：
B. Dwork
本系列的第一篇文章（此后记为NPM I，《数学年刊》94（1971），337 - 388页）中的曲线。正如当时所指出的，基本主题是富克斯 - 皮卡微分方程的p进可约性以及这种可约性与约化超曲面的泽塔函数的牛顿多边形之间的关系。即使在曲线的情形下，这些关系也没有被完全理解，在超奇异情形下所知甚少。我们在超曲面情形下的无知自然更为广泛。大致来说，所获得信息的量取决于牛顿多边形（约化超曲面的泽塔函数的中间维数因子的）接近“理想”最小形式的程度。对于下面引理5.1所涵盖的情形，存在最广泛的信息。除了下面的§6，我们将注意力限制在次数不能被p整除的超曲面上（参见[2]）。为了从另一个角度说明我们研究的性质，我们将陈述一个关于曲线的猜想，它可以用各种方式推广并扩展到更高维的簇。考虑一个在素域\(F_p\)上定义的平面曲线的代数系，并且以仿射\(N\)空间作为基空间。对于基空间中的\(X\)，令\(C_X\)为相应的曲线。我们假设对于一般的\(X\)，曲线\(C_X\)是非奇异的
curves in the first article (herafter denoted NPM I, Ann. of Math. 94 (1971), 337-388) of this series. As noted at that time the basic theme is the p-adic reducibility of Fuchs-Picard differential equations and the relation between this reducibility and the Newton polygon of the zeta function of the reduced hypersurface. These relations are not completely understood even in the case of curves where very little is known in the case of supersingularity. Our ignorance in the case of hypersurfaces is naturally more extensive. Roughly speaking the amount of information obtained depends upon the extent to which the Newton polygon (of the middle dimensional factor of the zeta function of the reduced hypersurfaces) approximate the "ideal" minimal form. The most extensive information exists for the case covered by Lemma 5.1 below. Except in ? 6 below, we restrict our attention to hypersurfaces of degree not divisible by p (cf. [2]). To indicate the nature of our investigation from another point of view we shall state a conjecture concerning curves which may be generalized in various ways and extended to varieties of higher dimension. Consider an algebraic system of plane curves defined over the prime field, Fp, and with affine N space as base space. For X in base space, let CR be the corresponding curve. We assume that for X generic the curve CR is non-singular