On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic
نویسندگان
چکیده
We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p > 3. The proof uses elliptic surfaces over P and inseparable base change. We then present adjusted inequalities. These follow from results of PesentiSzpiro. For characteristic 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over P. Our ideas are also related to supersingular surfaces (in Shioda’s sense).
منابع مشابه
On Davenport-Stothers inequalities in positive characteristic
We show that the Davenport-Stothers inequality fails in any characteristic p > 3. The proof uses elliptic surfaces over P and inseparable base change. We also comment on corrected inequalities. Our ideas are related to supersingular surfaces (in Shioda’s sense). For characteristic 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over P.
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