This is a study of the frequency of cerebral venous thrombosis (CVT) after covid. That's the rare brain blood clotting problem that is associated with an autoimmune reaction to platelets. There have been reports of rare cases of this happening, particularly in young women, who have received the adenovirus-vectored vaccines (J&J and AZ).
Rates of CVT after vaccination vary by country, but one study in Germany found 23 cases per million after first doses of AZ, and 0.5 per million after Pfizer. The background rate in Europe is about 1 case per 100,000 people per year. That comes out to about 0.8 per million per month, so the rate for Pfizer is pretty much the background rate.
The present study found that the risk of CVT after covid was 43 per million. So higher than the rate after AZ, but still rare. They also looked for CVT after flu and came up with about 11 per million. So even more rare after flu, but still probably above the background rate.
Rates in Europe after vaccination: https://www.medrxiv.org/content/10.1101/2021.04.30.21256383v2.full.pdf
Rates after Covid/Flu: https://www.medrxiv.org/content/10.1101/2021.04.27.21256153v1.full.pdf