The algebraic Novikov spectral sequence for topological modular forms

2024/04/08 by J. Francis Baer, Baer, J. Francis
Computer Science · Mathematics · #55Q10 #55T15 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2404.05573

openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the ℂ-motivic Adams spectral sequence for mmf/τ. Up to reindexing, this spectral sequence is isomorphic to the algebraic Novikov spectral sequence for topological modular forms. We give a full analysis of the inclusion and projection maps which occur in the long exact sequence induced by multiplication by τ on Adams E₂-pages. Our computation is totally algebraic and can be used to obtain the E₂-page of the Adams-Novikov spectral sequence for topological modular forms in a way that is independent from previous computations using the elliptic curves Hopf algebroid.

Related

• The \mathbb C-motivic Adams-Novikov spectral sequence for topological modular forms
• The homotopy of C-motivic modular forms
• The descent spectral sequence for topological modular forms
• The motivic Adams-Novikov spectral sequence at odd primes over ℂ and ℝ
• Explicit modular forms from the divided beta family