Abstract
Throughout this Chapter, k will denote an A-field; if v is a place of k, k v will denote the completion of k at v; if v is a finite place of k, we write r v for the maximal compact subring of k v and p v for the maximal ideal of r v , these being the subsets of k v respectively defined by |x| v ⩽1 and by |x| v < 1. We write P∞ for the set of the infinite places of k, and P for any finite set of places of k, containing P∞.
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© 1967 Springer-Verlag Berlin · Heidelberg
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Weil, A. (1967). Adeles. In: Basic Number Theory. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00046-5_4
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DOI: https://doi.org/10.1007/978-3-662-00046-5_4
Publisher Name: Springer, Berlin, Heidelberg
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