Goal -- Translate the infrastructure for Galois groups of number field to Galois groups of p-adic fields and implement some native algorithms to compute them.
Type -- advanced features
Priority -- Low (because it's long term and many of the capabilities already exist in Pari)
Difficulty -- High
Prerequisites -- varies depending on how much functionality is desired. For anything nontrivial, we have a lot of foundational work to do still.
Background --
Contributors -- David Roe
Progress - not started
Related Tickets --
Discussion
Tasks
- Create classes for Galois groups of local fields, parallel to those for number fields.
- Implement computation of Galois groups for unramified and tame extensions, both abstractly and with an action on the fields involved.
- Galois groups of wild extensions, higher ramification filtrations...