Hopf-Galois module structure of tamely ramified radical extensions of prime degree
نویسندگان
چکیده
منابع مشابه
Galois groups of tamely ramified p - extensions par Nigel BOSTON
Very little is known regarding the Galois group of the maximal p-extension unramified outside a finite set of primes S of a number field in the case that the primes above p are not in S. We describe methods to compute this group when it is finite and conjectural properties of it when it is infinite.
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Let p be a rational prime and S a finite set of rational primes. We are interested in the structure of GS(p), the Galois group of the maximal p-extension of Q unramified outside S (and ∞ if p = 2). In the case that p ∈ S, many GS(p) are known explicitly [12], but in the case that p ∈ S, very little is known. Throughout this report we shall assume that p ∈ S. The author developed methods to comp...
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Let K be a field of characteristic not p (an odd prime), containing a primitive p-th root of unity ζ, and let L = K[z] with x n − a the minimal polynomial of z over K: thus L|K is a Kummer extension, with cyclic Galois group G = 〈σ〉 acting on L via σ(z) = ζz. T. Kohl, 1998, showed that L|K has pn−1 Hopf Galois structures. In this paper we describe these Hopf Galois structures.
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The structure of an algebraic tamely ramified extension of a henselian valued field is studied. We will prove, in theorem 3.2, the following statement: A finite extension L/K is tamely ramified if and only if the field L is obtained from the maximal unramified extension T by adjoining the radicals m √ t, with t ∈ T, m ∈ N, m ≥ 1, (m, p) = 1, where p is the characteristic of the residue class fi...
متن کاملGALOIS MODULE STRUCTURE OF GALOIS COHOMOLOGY FOR EMBEDDABLE CYCLIC EXTENSIONS OF DEGREE p
Let p > 2 be prime, and let n,m ∈ N be given. For cyclic extensions E/F of degree p that contain a primitive pth root of unity, we show that the associated Fp[Gal(E/F )]-modules H(GE , μp) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p extension E/F , we give a more refined Fp[Gal(E/F )]-decomposition of H (GE , μp).
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2020
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2019.106231