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In "Differential operators on the flag varieties" (http://www.numdam.org/article/AST_1981__87-88__43_0.pdf) by Brylinski, he uses on page 53 a Künneth formula for local cohomology with support.

Unfortunately he gives no reference for the formula and so far I couldn't find any literature stating this theorem.

Does anyone know what the general statement is and where I could find it?

EDIT: I removed my guess for the formula.

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    $\begingroup$ I am confused. What is $Z\cap V_1$? Note that $V_1$ does not embed canonically into $V_1\times V_2$. $\endgroup$
    – Z. M
    Aug 4, 2021 at 14:40
  • $\begingroup$ That's a good point. Then I was too sloppy and I'm uncertain how the formula looks like. I will edit my question. $\endgroup$
    – KKD
    Aug 5, 2021 at 12:00
  • $\begingroup$ Did you check Bredon's "Sheaf Theory"? This is where a very general Künneth formula can be found. $\endgroup$ Aug 5, 2021 at 18:17

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