Step 1: Meaning of controversy.
A controversy is a prolonged public disagreement, debate, or heated discussion.
Step 2: Analyzing the options.
- Fight: Refers to physical conflict, not the same as controversy.
- Agreement: Opposite in meaning, so incorrect.
- Dispute: Correct, since both “controversy” and “dispute” imply disagreement.
- (Resolution: Refers to solving a problem, opposite meaning.
Step 3: Conclusion.
Thus, the correct synonym of controversy is “dispute.”
Final Answer:
\[
\boxed{\text{dispute}}
\]