Title: The m-step Solvable Mono-anabelian Geometry of Number Fields
Speaker: Mao Yu（China Three Gorges University）
Time: Friday, March 27, 2026, 10:30--11:30
Venue: Room 315, Gewu Building
Abstract:
In 1970s, Neukirch and Uchida proved the first result in anabelian geometry, i.e. the Neukirch-Uchida Theorem, which asserts that number fields are determined up to isomorphism from their (maximal prosolvable quotients of) absolute Galois groups. In 2019, Saidi and Tamagawa proved an m-step solvable version of the Neukirch-Uchida theorem for suitable integer m. However, the Neukirch-Uchida Theorem (resp. the Saidi-Tamagawa Theorem) does not yield a group-theoretic reconstruction of the number field starting from its maximal prosolvable (resp. maximal m-step solvable) Galois group. In 2021, Hoshi established a group-theoretic reconstruction of a number field (together with its maximal pro-solvable extension) starting from the maximal prosolvable Galois group. In this talk, we introduce a group-theoretic reconstruction of a number field (together with its maximal m-step solvable extension) starting from its maximal m + 9-step solvable Galois group for some integer m ≥ 3.
