• 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

1. Create classes for Galois groups of local fields, parallel to those for number fields.
2. Implement computation of Galois groups for unramified and tame extensions, both abstractly and with an action on the fields involved.
3. Galois groups of wild extensions, higher ramification filtrations...