Langlands's construction of the Taniyama group

Galois Conjugates of Special Points and Special Subvarieties in Shimura Varieties

“…Most of this is standard, except our use of the term 'Shimura pro-variety' for the inverse limit of the system of Shimura varieties associated with a given Shimura datum. Section 3 outlines key facts about the Serre and Taniyama groups from [11] and [14]. Section 4 states the conjecture of Langlands on conjugation of Shimura varieties, which is central to all the results of the paper.…”

Mixed automorphic vector bundles on Shimura varieties

“…The functor sending a Hodge structure (V, h) to the real Hodge structure (V ® M, h) defines a homomorphism /ι can : S ->• Θ R . The Serre group © and the homomorphism h CΆn have the following universal property: For any torus T over Q and homomorphism h : S -» T κ whose cocharacter is defined over a CM-field and whose weight is defined over Q there is a unique Q-rational homomorphism p : 6 -» T such that PK O /ι can = / & (see [25]). …”