We construct inductively an equivariant compactification of the algebraic group of Witt vectors of finite length over a field of characteristic p>0. We obtain smooth projective rational varieties defined over the field with p elements; the boundary is a divisor whose reduced subscheme has normal crossings. The Artin-Schreier-Witt isogeny extends to a finite cyclic cover of degree $p^n$ ramified at the boundary. This is used to give an extrinsic description of the local behavior of a separable cover of curves in char. p at a wildly ramified point whose inertia group is cyclic.
Linear systems attached to cyclic inertia
GARUTI, MARCO-ANDREA
2002
Abstract
We construct inductively an equivariant compactification of the algebraic group of Witt vectors of finite length over a field of characteristic p>0. We obtain smooth projective rational varieties defined over the field with p elements; the boundary is a divisor whose reduced subscheme has normal crossings. The Artin-Schreier-Witt isogeny extends to a finite cyclic cover of degree $p^n$ ramified at the boundary. This is used to give an extrinsic description of the local behavior of a separable cover of curves in char. p at a wildly ramified point whose inertia group is cyclic.File in questo prodotto:
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