The poem is split into different parts, each of which exposes participants in a murder. The first one to be introduced is one that is discussing moves in chess, primarily the Chigorin defense. Brodsky paints a background story to each participant, before mentioning how they can be the suspect of the murder. We are also introduced to people in the realm of acting among someone else, before we learn about a younger, teenage male who is staying with his grandparents and goes out one evening to get some ice cream. There is a threatening looking man that he brings down in what he feels is an act of defense. These here are the elements of seeing this poem as a murder mystery.
The final part of "Homage to Yalta," however, wraps up the ends to how a process like this is immensely inaccurate. In the act of accusing people, the majority of the accused are going to be incorrect. At the same time, ALL of them may be incorrect. This is what is being said in this particular case. Why this is deemed a "homage" is that we are introduced to people who are completely human and citizens of a community just like any other community across the globe. In a country like Russia, however, individuality is non-existent. Under a fearful leader such as Leonid Brezhnev, the act of individuality through writing is not going to be commended and would put someone like Brodsky in a position of danger.
"Homage to Yalta" is a murder mystery, but what Brodsky is making an attempt to convey is that it does not matter who did it. Instead, this poem is for the accused. It feeds to the frustration of living in a Communist Russia that, while denouncing Stalin, is still following the foundation that he has arranged.
Check out the first part of this post that I started a few months ago for more details regarding the structure and meaning (in my mind) behind this poem.