The unstable Adams spectral sequence is a spectral sequence that starts from algebraic information about the mod cohomology of a space as an unstable algebra over the Steenrod algebra , and converges, in good cases, to the -localized homotopy groups of . Bousfield and Don Davis looked at the case when was either of the infinite matrix groups or . Bousfield and Davis created algebraic spectral sequences and conjectured that they agreed with the unstable Adams spectral sequences for and . To this end the following algebraic decomposition must hold
where is the well known dyadic filtration of the -module given by the dyadic expansion of the powers of . This paper aims at showing that this decomposition holds for numerous values of and .
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Accepted:
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Keywords: Injective resolution, Projective resolution, Unstable Adams spectral sequence, Unstable modules
Thế Cường Nguyễn 1
@article{CRMATH_2023__361_G11_1789_0, author = {Thế Cường Nguyễn}, title = {On {Bousfield{\textquoteright}s} conjectures for the unstable {Adams} spectral sequence for $SO$ and $U$}, journal = {Comptes Rendus. Math\'ematique}, pages = {1789--1804}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.531}, language = {en}, }
Thế Cường Nguyễn. On Bousfield’s conjectures for the unstable Adams spectral sequence for $SO$ and $U$. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1789-1804. doi : 10.5802/crmath.531. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.531/
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