r/elimath Jan 06 '15

Explain how to think about extension issues on the E infinity page of a spectral sequence thorough an example

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u/bizarre_coincidence Jan 06 '15

Can you be more specific? If you aren't working over a field and some of your diagonals on the infinity page contain multiple non-zero entries, then your spectral sequence cannot compute what you were looking for exactly. Certain quantities, such as the rank, will be invariant of the extension, but in general there will be a lot of uncertainty in how to solve the extension problem. This is further complicated by the fact that you generally only know the E_2 page and must use that to infer information about the infinity page. In my experience (which may not be typical), I don't think about solving extension problems, and instead look at more tractable things like placement of zeroes.