The Witt kernels of purely inseparable quartic extensions
نویسندگان
چکیده
منابع مشابه
Hopf Galois structures on primitive purely inseparable extensions
Let L/K be a primitive purely inseparable extension of fields of characteristic p, [L : K] > p, p odd. It is well known that L/K is Hopf Galois for some Hopf algebra H, and it is suspected that L/K is Hopf Galois for numerous choices of H. We construct a family of K-Hopf algebras H for which L is an H-Galois object. For some choices of K we will exhibit an infinite number of such H. We provide ...
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It has recently been established that there are exactly seven Witt equivalence classes of quadratic number fields, and then all quadratic and cubic number fields have been classified with respect to Witt equivalence. In this paper we have classified number fields of degree four. Using this classification, we have proved the Conjecture of Szymiczek about the representability of Witt equivalence ...
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Let p be prime. Let L/K be a finite, totally ramified, purely inseparable extension of local fields, [L : K] = p, n ≥ 2. It is known that L/K is Hopf Galois for numerous Hopf algebras H, each of which can act on the extension in numerous ways. For a certain collection of such H we construct “Hopf Galois scaffolds” which allow us to obtain a Hopf analogue to the Normal Basis Theorem for L/K. The...
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The L-function of a non-degenerate twisted Witt extension is proved to be a polynomial. Its Newton polygon is proved to lie above the Hodge polygon of that extension. And the Newton polygons of the Gauss-Heilbronn sums are explicitly determined, generalizing the Stickelberger theorem.
متن کاملWitt Kernels of Quadratic Forms for Multiquadratic Extensions in Characteristic 2
Let F be a field of characteristic 2 and let K/F be a purely inseparable extension of exponent 1. We show that the extension is excellent for quadratic forms. Using the excellence we recover and extend results by Aravire and Laghribi who computed generators for the kernel Wq(K/F ) of the natural restriction map Wq(F ) → Wq(K) between the Witt groups of quadratic forms of F and K, respectively, ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.08.011