Lecture I: Liftings of Galois covers of smooth curves. (English) Zbl 0948.14021
From the paper: This and the following lecture are a report on the lifting problem of Galois covers of smooth curves from characteristic \(p>0\) to characteristic 0. The references are listed as: B. Green and M. Matignon, Compos. Math. 113, No. 3, 237-272 (1998; Zbl 0923.14006) and J. Am. Math. Soc. 12, No. 1, 269-303 (1999; Zbl 0923.14007); M. Matignon, Manuscr. Math. 99, No. 1, 93-109 (1999). This first lecture will focus on lifting problems, the main results are a local global principle and the positive answer to the lifting problem for \(p^2\)-cyclic covers generalizing a former result in \(p\)-cyclic case due to F. Oort, T. Sekiguchi, N. Suwa
For lecture II see the following review Zbl 0948.14022).
For lecture II see the following review Zbl 0948.14022).
MSC:
| 14H30 | Coverings of curves, fundamental group |
| 14G32 | Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) |
| 12F12 | Inverse Galois theory |
| 14L30 | Group actions on varieties or schemes (quotients) |
| 14H25 | Arithmetic ground fields for curves |
