Localizing the $E_2$ page of the Adams spectral sequence
| Autor: | Eva Belmont |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Conjecture
Ivanovskii spectral sequence Cartan–Eilenberg spectral sequence 010102 general mathematics MathematicsofComputing_GENERAL Margolis–Palmieri Adams spectral sequence 01 natural sciences Combinatorics Mathematics::K-Theory and Homology Adams spectral sequence 0103 physical sciences Line (geometry) Spectral sequence FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology 010307 mathematical physics Geometry and Topology 0101 mathematics Algebra over a field Element (category theory) 55T15 localized Ext Mathematics |
| Zdroj: | Algebr. Geom. Topol. 20, no. 4 (2020), 1965-2028 |
| Popis: | There is only one nontrivial localization of $\pi_*S_{(p)}$ (the chromatic localization at $v_0=p$), but there are infinitely many nontrivial localizations of the Adams $E_2$ page for the sphere. The first non-nilpotent element in the $E_2$ page after $v_0$ is $b_{10}\in \mathrm{Ext}_A^{2p(p-1)-2}(\mathbb{F}_p,\mathbb{F}_p)$. We work at $p=3$ and study $b_{10}^{-1}\mathrm{Ext}_P(\mathbb{F}_3,\mathbb{F}_3)$ (where $P$ is the algebra of dual reduced powers), which agrees with the infinite summand $\mathrm{Ext}_P(\mathbb{F}_3,\mathbb{F}_3)$ of $\mathrm{Ext}_A(\mathbb{F}_3,\mathbb{F}_3)$ above a line of slope ${1\over 23}$. We compute up to the $E_9$ page of an Adams spectral sequence in the category $\mathrm{Stable}(P)$ converging to $b_{10}^{-1}\mathrm{Ext}_P(\mathbb{F}_3,\mathbb{F}_3)$, and conjecture that the spectral sequence collapses at $E_9$. We also give a complete calculation of $b_{10}^{-1}\mathrm{Ext}_P^*(\mathbb{F}_3,\mathbb{F}_3[\xi_1^3])$. |
| Databáze: | OpenAIRE |
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