Published on *Max-Planck-Institut für Mathematik* (https://www.mpim-bonn.mpg.de)

Posted in

- Vortrag [1]

Speaker:

Mohamed Saidi
Zugehörigkeit:

University of Exeter/MPIM
Datum:

Die, 21/01/2020 - 14:00 - 15:00 A celebrated theorem of Neukirch and Uchida states that two number fields are isomorphic if their absolute Galois groups are isomorphic. The Grothendieck birational conjecture predicts a similar result for all finitely generated fields. This has been proved by Pop, using in an essential way the Neukirch-Uchida theorem for global fields.

In a recent work, joint with Akio Tamagawa, we prove that two number fields are isomorphic if their 3-step solvable Galois groups are isomorphic. More generally we prove that two finitely generated fields of (kronecker) dimension d are isomorphic if their 3+[3d(d+1)/2]-step solvable Galois groups are isomorphic. These results bring (birational) anabelian geometry close to class field theory.

In my talk I will explain the proof of our results in the number field case as well as the ideas and key ingredients of proof in general.

**Links:**

[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/de/node/3444

[3] https://www.mpim-bonn.mpg.de/de/node/5312