(Non)formality of cochains of absolute Galois groups

Dear Kirsten,

I am now visiting Ben Gurion University of the Negev in Be'er Sheva,
and Ido Efrat here kindly told me about your paper with
Michael Hopkins about splitting varieties for triple Massey products
http://www.math.harvard.edu/~kwickelg/papers/MPSV.pdf
I didn't yet have the time to read it properly, but there is one question
asked there which I think I know the answer to.

You are asking whether the cochain DG-algebra of an absolute Galois
group of a field F with the coefficients Z/2 is formal. The answer is,
I believe, "not in general", for the following reason.

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