Abelian geometric fundamental groups for curves over a p-adic field

For a curve X over a p-adic field k, using the class field theory of X due to S. Bloch and S. Saito we study the abelian geometric fundamental group π 1 ab (X) geo of X. In particular, we investigate a subgroup of π 1 ab (X) geo which classifies the geometric and abelian coverings of X which allow possible ramification over the special fiber of the model of X. Under the assumptions that X has a k-rational point, X has good reduction and its Jacobian variety has good ordinary reduction, we give some upper and lower bounds of this subgroup of π 1 ab (X) geo .