Some fundamental groups in the arithmetic of algebraic curves over finite fields.
Associated with some systems of unramified coverings of algebraic curves over finite fields there are spaces analogous to the universal covering transformation spaces. These spaces have also arithmetic features; they represent all the Frobeniuses in the systems. This theory can be applied to the reduction mod [unk] of the Shimura curves.
Ihara
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Department of Mathematics, Faculty of Sciences, University of Tokyo, Tokyo, 113, Japan.