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2020 Localizing the $E_2$ page of the Adams spectral sequence
Eva Belmont
Algebr. Geom. Topol. 20(4): 1965-2028 (2020). DOI: 10.2140/agt.2020.20.1965

Abstract

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 123. 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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Eva Belmont. "Localizing the $E_2$ page of the Adams spectral sequence." Algebr. Geom. Topol. 20 (4) 1965 - 2028, 2020. https://doi.org/10.2140/agt.2020.20.1965

Information

Received: 28 January 2019; Revised: 8 September 2019; Accepted: 13 November 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226709
MathSciNet: MR4127088
Digital Object Identifier: 10.2140/agt.2020.20.1965

Subjects:
Primary: 55T15

Rights: Copyright © 2020 Mathematical Sciences Publishers

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