Vavilov was awarded the Order of Lenin under Stalin and his research institute was established under Stalin as well (that Lysenko came up in).

There's unfortunately not a lot of easily accessible information on the investigation of Vavilov, but if:

• you're not a member of the party
• you spend a lot of time on international field trips to collect seeds
• you spend a lot of time in western countries for research collaboration, and
• you're the head of the USSR agricultural institute during the Soviet famine of 1930-33

You should probably have resigned and kept doing field work.

It's reported that Stalin was directly involved in Vavilov's arrest, intervening to support Lysenko, but it's unclear whether this was actually the case - 8 years later, Stalin edited a speech of Lysenko to remove references to what's considered a key factor in Lysenko's popularity

In his original manuscript Lysenko did portray genetics as "bourgeois science" and tried to reduce his conflict with geneticists to the contra-dictions inherent in class antagonisms. But in editing Lysenko's text Stalin deleted the discourse about the class character of science and completely eliminated the word bourgeois in reference to science (it was used in Lysenko's original text twenty-eight times).