Abstract
Let G be a finite p -group and F a field of characteristic p . We filter the cochain complex of a free G -space with coefficients in F by powers of the augmentation ideal of F G . We show that the cup product induces a multiplicative structure on the arising spectral sequence and compute the E 1 -page as a bigraded algebra. As an application, we prove that recent counterexamples of Iyengar and Walker to an algebraic version of Carlsson's conjecture can not be realized topologically.
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