 Künneth spectral sequence (source code)

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= Künneth spectral sequence
{c}
{title2=$E_2^{p,q}=\operatorname{Tor}_{-p}^R(H^qP,M)\Rightarrow H^{p+q}(P\otimes_RM)$}

For a bounded complex $P$ of projective right modules and a left module $M$ of finite <projective dimension>, a finite projective resolution of $M$ yields a bounded <double cochain complex>. Its two <spectral sequences> give the displayed abutment. Over a noncommutative ring, the handedness of the two tensor factors is essential.

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