Supercuspidal representations in the cohomology of Drinfel'd upper half spaces; elaboration of Carayol's program

摘要

Let F be a finite extension of Qp. In his reconsideration [Dr] of Cherednik's theorem on p-adic uniformization of Shimura curves, Drinfel'd constructed an inverse system ∑N of rigid-analytic etale Galois coverings of the nonarchimedean upper half space ΩPn-1F, indexed by positive integers N. These coverings are equivariant for the action of GL (n, F) and for the group Bx of units in a division algebra B over F with invariant 1. The introduction to [Dr] suggested that every supercuspidal representation of GL (n, F) was realized in the "cohomology" of these Galois coverings. A more precise conjecture was stated by Carayol in [Ca].