Galois module structure of cohomology groups for tamely ramified coverings of algebraic varieties
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...
متن کاملGalois Module Structure of Galois Cohomology
Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group GF of F . We determine the structure of the cohomology group H(U, Fp) as an Fp[GF /U ]-module for all n ∈ N. Previously this structure was known only for n = 1, and until recently the structure even of H(U, Fp) was determined only for F a local field, a case se...
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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 Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90032-6