1995
DOI: 10.1017/s0305004100072923
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Cyclotomic Galois module structure and the second Chinburg invariant

Abstract: We study the second Chinburg invariant of a Galois extension of number fields. The Chinburg invariant lies in the class-group of the integral group-ring of the Galois group of the extension. A procedure is given whereby to evaluate the invariant in the case of the real cyclotomic case of regular prime power conductor and their subextensions of p-power degree. The invariant is shown to be zero in the latter cases, which yields new examples giving an affirmative answer to a question of Chinburg ([1], p. 358) whi… Show more

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Cited by 3 publications
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“…The second Chinburg invariant (no(L/ K, 2) in our notation) is constructed from a projective Z[G(L/ K)]module, X, and the classical fundamental classes of local class field theory (see [131] Chapter 7). In a similar manner, one may use the fundamental classes of , [38], [138], [139] This is to be interpreted as meaning that X is the intersection of L with the product of its P-completions, Xp, where both are considered as subgroups of the adeIes. Hence X is a locally free OK [G(L/ K)]-module whose P-completion is…”
Section: The Higher K-theory Invariants Ns(lj K 2)mentioning
confidence: 99%
“…The second Chinburg invariant (no(L/ K, 2) in our notation) is constructed from a projective Z[G(L/ K)]module, X, and the classical fundamental classes of local class field theory (see [131] Chapter 7). In a similar manner, one may use the fundamental classes of , [38], [138], [139] This is to be interpreted as meaning that X is the intersection of L with the product of its P-completions, Xp, where both are considered as subgroups of the adeIes. Hence X is a locally free OK [G(L/ K)]-module whose P-completion is…”
Section: The Higher K-theory Invariants Ns(lj K 2)mentioning
confidence: 99%