Galois structure of infinite places in a number field. (Structure galoisienne des places infinies d’un corps de nombres.) (French) Zbl 0805.11082

Let \(N\) be a finite extension of \(\mathbb{Q}\) and let \(\Gamma\) be a group of automorphisms of \(N\). Let \(R(\Gamma)\) be the group of characters of \(\Gamma\). The author observes that in the theory of Artin \(L\)-functions, there appear homomorphisms from \(R(\Gamma)\) into \(\mathbb{Z}\) and homomorphisms from \(R(\Gamma)\) into \(\mathbb{C}^ \times\). These may be interpreted in terms of \(K\)-groups \(K_0\) and \(K_1\). The author then shows how the regulator, discriminant, class number, etc., can be interpreted in terms of \(\Gamma\)-modules constructed from the set of embeddings of \(N\) into \(\mathbb{C}\) and from the archimedean places of \(N\).


11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
11R42 Zeta functions and \(L\)-functions of number fields
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