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Localizing the $E_2$ page of the Adams spectral sequence

Eva Belmont

Algebraic & Geometric Topology 20 (2020) 1965–2028

There is only one nontrivial localization of πS(p) (the chromatic localization at v0 = p), but there are infinitely many nontrivial localizations of the Adams E2 page for the sphere. The first nonnilpotent element in the E2 page after v0 is b10 ExtA2,2p(p1)(𝔽p, 𝔽p). We work at p = 3 and study b101 ExtP,(𝔽3, 𝔽3) (where P is the algebra of dual reduced powers), which agrees with the infinite summand ExtP,(𝔽3, 𝔽3) of ExtA,(𝔽3, 𝔽3) above a line of slope 1 23. We compute up to the E9 page of an Adams spectral sequence in the category Stable(P) converging to b101 ExtP,(𝔽3, 𝔽3), and conjecture that the spectral sequence collapses at E9. We also give a complete calculation of b101 ExtP,(𝔽3, 𝔽3[ξ13]).

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Adams spectral sequence, localized Ext, Cartan–Eilenberg spectral sequence, Ivanovskii spectral sequence, Margolis–Palmieri Adams spectral sequence
Mathematical Subject Classification 2010
Primary: 55T15
Received: 28 January 2019
Revised: 8 September 2019
Accepted: 13 November 2019
Published: 20 July 2020
Eva Belmont
Department of Mathematics
Northwestern University
Evanston, IL
United States