Spectral Sequences
Filtered complexes, Grothendieck spectral sequences, and convergence.
Spectral Sequences. Filtered complexes, Grothendieck spectral sequences, and convergence.
Foundations and canonical references
The standard treatments of spectral sequences approach the subject from complementary angles. Mccleary, A User’s Guide to Spectral Sequences (2001) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Weibel, An Introduction to Homological Algebra (1994) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for spectral sequences include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2001A User's Guide to Spectral Sequencesmccleary-2001
- textbook · primary · 1994An Introduction to Homological Algebraweibel-1994
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