In mathematics, the Taniyama group is a group that is an extension of the absolute Galois group of the rationals by the Serre group . It was introduced by Langlands (1977 ) using an observation by Deligne , and named after Yutaka Taniyama . It was intended to be the group scheme whose representations correspond to the (hypothetical) CM motives over the field Q of rational numbers.
Deligne, Pierre ; Milne, James S. ; Ogus, Arthur ; Shih, Kuang-yen (1982), "Langlands's Construction of the Taniyama Group", Hodge cycles, motives, and Shimura varieties. (PDF) , Lecture Notes in Mathematics, vol. 900, Berlin-New York: Springer-Verlag, doi :10.1007/978-3-540-38955-2_14 , ISBN 3-540-11174-3 , MR 0654325
Langlands, R. P. (1977), "Automorphic representations, Shimura varieties, and motives. Ein Märchen", Automorphic forms, representations and L-functions , Proc. Sympos. Pure Math., vol. 33, pp. 205–246, ISBN 0-8218-1437-0 , MR 0546619