UPDATE: After posting the question, I found out, to my great disappointment, that Manhunt Unabomber is only loosely based on real events, so I'm rephrasing the question:
Where is the Slavic homeland, according to linguists, and how do they know that? Is there any truth to the story relayed in Manhunt Unabomber (below)?
In Manhunt Unabomber (presumably based on real events), a Stanford linguist explains the origin of Slavs. Her story goes:
Around the year 600, Slavic peoples suddenly appeared all over Europe: Germany, Poland, Serbia, Russia, but nobody could figure out where they came from. It was a huge historical mystery, until they started looking at language, and they realized that Proto-Slavic was missing words for certain kinds of trees -- they had to borrow words for "oak" and "beech" and "pine"... The Pripyat river valley in Ukraine, it's basically this huge swamp, the only place in Europe where there are no trees!
It's an interesting theory, but there is one problem with it. Pripyat is surrounded by trees. You can't find pictures of Pripyat (a city on the Pripyat river, evacuated following the Chernobyl disaster), without trees in them.
What happened? Did trees appear where there weren't any in 500AD?