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Why are spectral sequences called "spectral"? Is that use of "spectral" related to other uses in math, such as spectra in homotopy theory, the spectrum of a ring in algebraic geometry or the spectrum of an operator? Why are those things called spectral, for that matter?

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    See here: http://mathoverflow.net/questions/17357/what-is-so-spectral-about-spectral-sequences2011-01-29
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    @Theo Buehler I think you should add your comment as an answer because if the answers to the MO question and the links given there end up answering the OP's question, he'll have no way of accepting it as an answer.2011-01-29
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    @Adrián Barquero: You're right. Done.2011-01-29

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As per Adrián Barquero's request, I post my comment as an answer (even if I think that it doesn't answer the question but rather indicates that the answer isn't really known).

See the related discussion on Math Overflow.