NEW CASES OF p-ADIC UNIFORMIZATION
نویسندگان
چکیده
The subject matter of p-adic uniformization of Shimura varieties starts with Cherednik’s paper [6] in 1976, although a more thorough historical account would certainly involve at least the names of Mumford and Tate. Cherednik’s theorem states that the Shimura curve associated to a quaternion algebra B over a totally real field F which is split at precisely one archimedean place v of F (and ramified at all other archimedean places), and is ramified at a non-archimedean place w of residue characteristic p admits p-adic uniformization by the Drinfeld halfplane associated to Fw, provided that the level structure is prime to p. In adelic terms, this theorem may be formulated more precisely as follows. Let C be an open compact subgroup of (B ⊗F AF )× of the form C = C · Cw, where Cw ⊂ (B ⊗F Fw) is maximal compact and C ⊂ (B ⊗F A F )×. Let SC be the associated Shimura curve. It has a canonical model over F and its set of complex points, for the F -algebra structure on C given by v, has a complex uniformization SC(C) = B×\ [ X× (B ⊗F AF )×/C ] ,
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