The Absolute Anabelian Geometry of Hyperbolic Curves
نویسندگان
چکیده
Let XK be a hyperbolic curve (cf. §0 below) over a field K of characteristic 0. Denote its algebraic fundamental group by ΠXK . Thus, we have a natural surjection ΠXK GK of ΠXK onto the absolute Galois group GK of K. When K is a finite extension of Q or Qp, and one holds GK fixed, then it is known (cf. [Tama1], [Mzk6]; Theorem 1.3.4 of the present manuscript) that one may recover the curve XK in a functorial fashion from ΠXK . This sort of result may be thought of as a “relative result” (i.e., over GK). Then the question naturally arises:
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تاریخ انتشار 2003