I would also be interested in more sources on this topic. The wikipedia page on Vavilov links this source on the Soviet view of genetics, but it has a very clear anti-communist bias and some obvious nonsense. I only realized this most of the way through typing my comment but apparently the author joined the USSR branch of Amnesty International in 1981, and was the chairman from 1985-1988. My favorites are claiming 10 million peasants were arrested and exiled or shot during collectivization (source: Winston Churchill, The Second World War, vol. 4) and this line:

Thus, Party leaders began doing what scientists always tried to avoid: turning scientific sessions into forums for resolving political tasks.

Anyways, the article is interesting even if I'm skeptical of it's accuracy. It seems as though there was a lot of debate around genetics in the Soviet Union at the time, which makes sense to me from a layperson's perspective at least. From what I understand, modern genetics was a relatively new science at the time, and considering the role of eugenics and Social Darwinism in Nazi ideology, I think it's reasonable that some Soviet scientists were skeptical. If I am incorrect here, I'd appreciate it if someone could correct me.

Vavilov himself certainly spoke highly of Soviet science. Here's a telegram he sent to The New York Times:

The lie about Soviet science and Soviet scientists conscientiously working for the cause of socialism has become the specialty of certain organs of the foreign press…. On many occasions I gave reports in the press and orally in many cities of the USA about Soviet science, about the exceptional possibilities granted to Soviet scientists, about the role of science in our country, and about the tremendous progress of science during the Soviet period.

From a small institution during the Tsarist period—the Bureau of Applied Botany—the Institute of Plant Industry that I am in charge of has grown during the Soviet period into a most prestigious scientific institution having few equals in scale in the world. Its staff of about 65 people during the Tsarist period at the present time has reached 1,700 when all its branches in the outlying areas are included. The institute’s budget has gone from 50 thousand rubles to 14 million rubles...

We argue, discuss existing theories in genetics and in selection [plant breeding—V.S.] methods, we summon each other to Socialist competition, and I have to tell you frankly, this is a great stimulus, which significantly increases the level of work…

I more than many other people am obliged to the government of the USSR for its great attention to the institute I head and to my personal work.

As a faithful son of the Soviet country, I consider it my duty and good fortune to work for the good of my native land and give my entire being to science in the USSR.

Sweeping aside as vile slander of dubious origin your report about me and the fabrications that in the USSR intellectual freedom allegedly does not exist, I insist on the publication of the present telegram in your newspaper.

Academician N. I. Vavilov (1936).

As for his imprisonment, it seems like he was arrested for foreign espionage and sabotage? It's pretty difficult for me to find a more concrete answer than this, as this story seems to be an anti-communist favorite and there are tons of articles propagandizing about Stalinism around it. Again if anyone has better sources, or if @GayTuckerCarlson@hexbear.net wants to link a source, I'd appreciate it. I got sucked into this and spent more time on it than I wanted to already.