Ramified extensions of degree p and their Hopf–Galois module structure
نویسندگان
چکیده
منابع مشابه
GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF EXTENSIONS OF DEGREE p
For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree p. The foundation of the study of the maximal p-extensions of fields K containing a primitive pth root of unity is a group of the pth-power classes of the field: by Kummer theory this group describe...
متن کاملGALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE p
In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F .
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).
متن کاملSe p 20 04 GALOIS MODULE STRUCTURE OF p TH - POWER CLASSES OF CYCLIC EXTENSIONS OF DEGREE
In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F .
متن کاملGalois 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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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2018
ISSN: 1246-7405,2118-8572
DOI: 10.5802/jtnb.1014