A generalization of the Oort conjecture
The Oort conjecture (now a theorem of Obus–Wewers and Pop) states that if $k$ is an algebraically closed field of characteristic $p$, then any cyclic branched cover of smooth projective $k$-curves lifts to characteristic zero. This is equivalent to the local Oort conjecture, which states that all cy...
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Veröffentlicht in: | Commentarii mathematici Helvetici 2017-01, Vol.92 (3), p.551-620 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The Oort conjecture (now a theorem of Obus–Wewers and Pop) states that if $k$ is an algebraically closed field of characteristic $p$, then any cyclic branched cover of smooth projective $k$-curves lifts to characteristic zero. This is equivalent to the local Oort conjecture, which states that all cyclic extensions of $k[[t]]$ lift to characteristic zero. We generalize the local Oort conjecture to the case of Galois extensions with cyclic $p$-Sylow subgroups, reduce the conjecture to a pure characteristic $p$ statement, and prove it in several cases. In particular, we show that $D_9$ is a so-called local Oort group. |
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ISSN: | 0010-2571 1420-8946 |
DOI: | 10.4171/CMH/419 |