关于Davenport-Stothers不等式与正特征椭圆曲面
On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic
摘要：
证明了特征为0的Davenport-Stothers不等式在任何特征p>3时都不成立。证明使用椭圆曲面上的投影线和不可分的基地变化。然后，我们提出调整的不平等。这些结果来自Pesenti-Szpiro的结果。对于特征2和特征3，我们得到了关于射影直线上椭圆曲面的极大奇异纤维的类似结果。我们的想法也与超奇异表面（在Shioda的意义）。
英文摘要：
We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p>3. The proof uses elliptic surfaces over the projective line and inseparable base change. We then present adjusted inequalities. These follow from results of Pesenti-Szpiro. For characteristic 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over the projective line. Our ideas are also related to supersingular surfaces (in Shioda's sense).
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