September 8, 2025 |
Anabelian properties of tame fundamental groups of singular curvesMurotani Takahiro, Kyoto Institute of Technology, Japan RIMS Kyoto (Room 110) + Zoom · JP: 15:30 · FR: 08:30It is known that the tame fundamental group of a connected singular curve over a separably closed field is isomorphic to the free profinite product of some free profinite group (of finite rank) and the tame fundamental groups of the irreducible components of the normalization of the curve. By using this, and by applying the Grothendieck conjecture for hyperbolic curves over finite fields (proved by Tamagawa and Mochizuki) and generalized sub-\(p\)-adic fields (proved by Mochizuki), we reconstruct the isomorphism classes of the normalizations of curves (possibly reducible or singular) over these fields from the tame fundamental groups of the curves. |
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