Localizing the E2 page of the Adams spectral sequence

Belmont, Eva¹

¹Department of Mathematics, Northwestern University, Evanston, IL, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 1965-2028

Résumé

There is only one nontrivial localization of π∗S(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(p−1)(𝔽p, 𝔽p). We work at p = 3 and study b10−1 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 b10−1 ExtP∗,∗(𝔽3, 𝔽3), and conjecture that the spectral sequence collapses at E9. We also give a complete calculation of b10−1 ExtP∗,∗(𝔽3, 𝔽3[ξ13]).

Détail

DOI : 10.2140/agt.2020.20.1965

Classification : 55T15
Keywords: Adams spectral sequence, localized Ext, Cartan–Eilenberg spectral sequence, Ivanovskii spectral sequence, Margolis–Palmieri Adams spectral sequence

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