A spectral sequence is a mathematical tool used in algebraic topology, homological algebra, and related fields to compute homology or cohomology groups that may be difficult to compute directly. It provides a method to systematically approximate these groups through a sequence of pages (typically indexed by integers) and associated differentials.
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A succession of bigraded pages with . In the cohomological convention, the differential has bidegree . A filtered complex produces such successive approximations to its cohomology.