Automorphisms of curves and Weierstrass semigroups for Harbater-Katz-Gabber covers. (English) Zbl 1411.14031
Let \(k\) be a an algebraically closed field of characteristic \(p>0\). The article focuses on properties of Harbater-Katz-Gabber (HKG) \(p\)-covers, which are Galois covers of the projective line with a unique wildly ramified point and no other ramification. The interest for such covers comes from the HKG compactification theorem [D. Harbater, Commun. Algebra 8, 1095–1125 (1980; Zbl 0471.14011)], [N. M. Katz, Ann. Inst. Fourier 36, No. 4, 69–106 (1986; Zbl 0564.14013)] which asserts that starting from a \(p\)-group \(G\) acting on \(k[[t]]\), one can find such a HKG \(p\)-cover \(X \to \mathbb{P}^1\) such that \(\text{Gal}(X/\mathbb{P}^1)=G\). After a very complete introduction on the topic, the main goals of the authors are:
- ●
- characterizing the lower ramification jumps in terms of the pole numbers at the unique ramification point;
- ●
- studying the Galois module structure of spaces of poly-differentials of HKG \(p\)-covers.
Reviewer: Christophe Ritzenthaler (Marseille)
MSC:
| 14H37 | Automorphisms of curves |
| 14H55 | Riemann surfaces; Weierstrass points; gap sequences |
| 11G20 | Curves over finite and local fields |
| 20M14 | Commutative semigroups |
| 14H10 | Families, moduli of curves (algebraic) |
Keywords:
automorphisms; curves; numerical semigroups; Harbater-Katz-Gabber covers; zero \(p\)-rank; big actions; Galois module structureReferences:
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