Wild ramification and a vanishing cycles formula. (English) Zbl 1060.14052
K. Kato proved a formula which compares the dimension of the space of vanishing cycles in a finite morphism between formal germs of curves over a complete discrete valuation ring [Duke Math. J. 55, 629–659 (1987; Zbl 0665.14005)]. Kato’s formula is explicit only in the case where the morphism in question is generically separable on the level of special fibres.
In the paper under review, using formal patching techniques à la Harbater, the author proves an analogous explicit formula in the case of a Galois cover of degree \(p\) between formal germs of curves over a complete discrete valuation ring of unequal characteristic \((0,p)\). This formula includes the case when one has inseparability on the level of special fibres and has applications in the study of semi-stable reduction of Galois covers of curves.
In the paper under review, using formal patching techniques à la Harbater, the author proves an analogous explicit formula in the case of a Galois cover of degree \(p\) between formal germs of curves over a complete discrete valuation ring of unequal characteristic \((0,p)\). This formula includes the case when one has inseparability on the level of special fibres and has applications in the study of semi-stable reduction of Galois covers of curves.
Reviewer: Lucian Bădescu (Genova)
MSC:
| 14J10 | Families, moduli, classification: algebraic theory |
| 14H10 | Families, moduli of curves (algebraic) |
| 14B05 | Singularities in algebraic geometry |
Citations:
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