I am currently looking for a Masters thesis subject in number theory. My favourite subjects are algebraic number theory and cohomologies (I only studied De Rham cohomology).
I've been lately reading some papers around classical BSD and p-adic analogue (conjecture based on Tate–Shafarevich group), Selmer groups, Goldfeld's conjecture... before I actually study elliptic curves and modular forms but I have few notions.
So far, I am not being able to identify a subject around BSD. My approach have been reading papers, and see if there is a need to generalize to a wider range of objects, or maybe the opposite way, try to apply a general theorem to specific type of curves. I think my failure is expectable: I am new to the subject and I don't know what's really the purpose of a Masters thesis? Find something new or rather study the state of the art of a known problem.
Could anyone help me? advices, references are more than welcome.
P.S.: W.Stein's blog suggests few topics but even him is not sure whether those are unsolved problems. I don't know which topics might be feasible in the time span of a Masters thesis.
Thank you for your help.