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.
2002
Arithmetic Fundamental Groups and Noncommutative Algebra
9780821820360
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1349274
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