Mild pro-p-Galois groups of algebraic number fields
Final Report Abstract
Having the possibility to interact directly with John Labute, Jan Minč and other collaborators was a key success factor for the project. Apart from the results published, possible future projects have been discussed with researchers also outside of McGill university. Due to the limited duration of the stay in Montréal, it was not possible to get all of those projects on track yet, but this has led - and expectedly will lead - to further achievements in future projects. Regarding the questions originally formulated in the application, some good progress could be made. Recent developments had led to a slight shift of parts of the mentioned topics towards the theory of p-adic Galois representations. Starting to work on the tame Fontaine-Mazur conjecture was very promising. Despite some progress made however, this has not led to the desired breakthrough. At the same time, surprisingly different questions could be settled which had not been in scope originally. I have profited to a high extent from excellent working conditions at McGill University. Joining the Québec-Vermont Number Theory seminar hosted in Montréal, I had the chance to exchange with various leading experts in the field. Among other highlights, I was invited speaker at the Winter Conference of the Canadian Mathematical Society.
Publications
- On p-class groups and the Fontaine-Mazur conjecture. Mathematical Research Letters Volume 21 (2014), Number 3, Pages: 469 – 477
J. Gärtner
(See online at https://dx.doi.org/ http://dx.doi.org/10.4310/MRL.2014.v21.n3.a5) - Higher Massey products in the cohomology of mild pro-pgroups. J. Algebra, 422:788–820, 2015
J. Gärtner
(See online at https://doi.org/10.1016/j.jalgebra.2014.07.023)
