In-Person and Online Talk 

In this talk, I will specify a Turing machine T and prove the following about it.

1. On input C/K a smooth projective hyperbolic curve over a number field, if T halts, then its output is C(K).

2. The Hodge, Tate, and Fontaine-Mazur conjectures imply T always halts.

(Joint work with Brian Lawrence.)