An extension of the Grothendieck conjecture on the maximal geometrically m-step solvable quotients of arithmetic fundamental groups
アブストラクト
The Grothendieck conjecture states that "the information of hyperbolic curves is reconstructed group theoretically from their arithmetic fundamental group". This conjecture is one of the most important problems in Anabelian geometry. It was solved in the 1990s by Hiroaki Nakamura, Akio Tamagawa, Shinichi Mochizuki and others. In this talk, I will discuss the m-step solvable version of the Grothendieck conjecture (i.e. "the information of hyperbolic curves is reconstructed group theoretically from the maximal geometrically m-step solvable quotient of their arithmetic fundamental group") and present the current status of this conjecture.