A verb for 'talking about something very briefly and roughly'?

The use of roughly is somewhat subjective, but I would use summarize:

[Merriam-Webster]
transitive verb
: to tell in or reduce to a summary

intransitive verb
: to make a summary

summary
1 : COMPREHENSIVE
especially : covering the main points succinctly
2 a : done without delay or formality : quickly executed
// a summary dismissal
2 b : of, relating to, or using a summary proceeding
// a summary trial

So, the example sentence would become:

In the end, I summarize the implication of my view for that field of study.

In a paper or book, a summary is used at the end to sum up what you've said. It can include everything you've said, or only a certain component—such as the implications of a thesis. It depends on what you're emphasizing.

This is in contrast to an outline, which almost always only comes before something about to be discussed in detail.

Touch upon seems to fit...

https://www.merriam-webster.com/dictionary/touch%20on%2Fupon

to briefly talk or write about (something) : to mention (something) briefly

“The reports touched on many important points.”

“She touches upon the issue in the article but never fully explains it.”

In your example:

In the end I touch upon the implication of my view for that field of study.

The choice is very wide. You could search a thesaurus and pick what seems to you suitable from that. It does not have to be a word for 'talk'. So you have been offered touch upon, which would do fine as a familiar metaphorical expression. In that vein, you could 'sketch (or shade) in'; or 'outline'.

I notice, however, that you use the singular "implication". If there is only one implication, would it be anything other than brief?