Details
| Original language | English |
|---|---|
| Pages (from-to) | 499-522 |
| Number of pages | 24 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 59 |
| Issue number | 4 |
| Publication status | Published - Dec 2008 |
| Externally published | Yes |
Abstract
Keywords
- elliptic surfaces, Davenport-Stothers inequalities
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Quarterly Journal of Mathematics, Vol. 59, No. 4, 12.2008, p. 499-522.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On Davenport-Stothers inequalities and elliptic surfaces in positive characteristic
AU - Schütt, Matthias
AU - Schweizer, Andreas
N1 - Funding information: This paper benefitted greatly from discussions with B. van Geemen and T. Shioda while the first author enjoyed the hospitality of Dipartimento di Matematica ‘Frederico Enriques’ of Milano University. Support from the CRTN-network ‘Arithmetic Algebraic Geometry’ is gratefully acknowledged. During the revision and extension of the paper, the first author was generously funded by DFG under grant ‘SCHU 2266/2-1’. We also thank I. Bouw for explanations about reduction properties of base changes, and C. Liedtke for pointing out the reference to Illusie’s paper.
PY - 2008/12
Y1 - 2008/12
N2 - We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p > 3. The proof uses elliptic surfaces over ℙ1 and inseparable base change. We then present adjusted inequalities. These follow from results of Pesenti and Szpiro. For characteristics 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over ℙ1. Our ideas are also related to supersingular surfaces (in Shioda's sense).
AB - We show that the Davenport-Stothers inequality from characteristic 0 fails in any characteristic p > 3. The proof uses elliptic surfaces over ℙ1 and inseparable base change. We then present adjusted inequalities. These follow from results of Pesenti and Szpiro. For characteristics 2 and 3, we achieve a similar result in terms of the maximal singular fibres of elliptic surfaces over ℙ1. Our ideas are also related to supersingular surfaces (in Shioda's sense).
KW - elliptic surfaces
KW - Davenport-Stothers inequalities
UR - http://www.scopus.com/inward/record.url?scp=56749158461&partnerID=8YFLogxK
UR - https://arxiv.org/abs/math/0608427
U2 - 10.1093/qmath/ham048
DO - 10.1093/qmath/ham048
M3 - Article
AN - SCOPUS:56749158461
VL - 59
SP - 499
EP - 522
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 4
ER -