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.

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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.

The word succinct seems a perfect fit.

https://www.merriam-webster.com/dictionary/succinct

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?