Spectral duality for block cohomology

AbstractThroughout this paper k denotes an algebraically closed field of characteristic p > 0, G denotes a finite group, B denotes a p-block of G corresponding to the indecomposable algebra summand kB of kG, D denotes a defect group of B (it is unique up to conjugacy in G), p denotes the p-rank of D (that is, the maximum of the ranks of its elementary abelian p-subgroups) and S, T denote kB-modules. A graded polynomial subalgebra R of H∗(G, k) is specified by taking p algebraically independent canonical homogeneous elements, which are certain Chern classes, to be its generators. A spectral sequence is constructed with ExtR∗∗(ExtkB∗(S, T), R) as its E2 term and with ExtkB∗(T, S), with a displaced grading, as its abutment. The latter is thus naturally filtered. A brief account of the relevant algebraic topology, commutative algebra and homological algebra is given