Remark 6.0.1. Spelling note.
There is a lack of consensus regarding the presence or absence of accents in the words adèle and idèle, in either English or French. The term idèle appears to be a contraction of ideal element; it makes its first appearance, with the accent, in Chevalley’s 1940 paper [6] written in French. The term adèle appeared in the 1950s, possibly as a contraction of additive idèle; it appears to have been suggested by Weil as a replacement for Tate’s term valuation vector and Chevalley’s term repartition. Based on this history, we have opted for the accented spellings here; however, we drop the accent in inflected forms such as adelic.
