The Adams Spectral Sequence for Topological Modular Forms

2021 ◽  
Author(s):  
Robert Bruner ◽  
John Rognes
Keyword(s):  
Spectral Sequence ◽  
Modular Forms ◽  
Adams Spectral Sequence ◽  
Topological Modular Forms

scholarly journals On the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$

2021 ◽  
Author(s):  
Dominic Leon Culver ◽  
Paul VanKoughnett
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence

AbstractAs a step towards understanding the $$\mathrm {tmf}$$ tmf -based Adams spectral sequence, we compute the K(1)-local homotopy of $$\mathrm {tmf}\wedge \mathrm {tmf}$$ tmf ∧ tmf , using a small presentation of $$L_{K(1)}\mathrm {tmf}$$ L K ( 1 ) tmf due to Hopkins. We also describe the K(1)-local $$\mathrm {tmf}$$ tmf -based Adams spectral sequence.

scholarly journals Hecke Operations and the Adams E2-Term Based on Elliptic Cohomology

1999 ◽  
Vol 42 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Andrew Baker
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Hecke Operators ◽  
Elliptic Cohomology

AbstractHecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.

scholarly journals The Picard group of topological modular forms via descent theory

2016 ◽  
Vol 20 (6) ◽  
pp. 3133-3217 ◽  
Author(s):  
Akhil Mathew ◽  
Vesna Stojanoska
Keyword(s):  
Modular Forms ◽  
Picard Group ◽  
Descent Theory ◽  
Topological Modular Forms

Some infinite families in the stable homotopy of spheres

1987 ◽  
Vol 101 (3) ◽  
pp. 477-485 ◽  
Author(s):  
Wen-Hsiung Lin
Keyword(s):  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Stable Homotopy Of Spheres

The classical Adams spectral sequence [1] has been an important tool in the computation of the stable homotopy groups of spheres . In this paper we make another contribution to this computation.

scholarly journals ON THE DOUBLE TRANSFER AND THE f-INVARIANT

2012 ◽  
Vol 54 (3) ◽  
pp. 547-577
Author(s):  
GEOFFREY POWELL
Keyword(s):  
Spectral Sequence ◽  
Modular Forms ◽  
Homotopy Theory ◽  
Transfer Map

AbstractThe purpose of this paper is to investigate the algebraic double S1-transfer, in particular the classes in the two-line of the Adams–Novikov spectral sequence which are the image of comodule primitives of the MU-homology of ℂP∞ × ℂP∞ via the algebraic double transfer. These classes are analysed by two related approaches: the first, p-locally for p ≥ 3, by using the morphism induced in MU-homology by the chromatic factorisation of the double transfer map together with the f′-invariant of Behrens (for p ≥ 5) (M. Behrens, Congruences between modular forms given by the divided β-family in homotopy theory, Geom. Topol.13(1) (2009), 319–357). The second approach (after inverting 6) uses the algebraic double transfer and the f-invariant of Laures (G. Laures, The topological q-expansion principle, Topology38(2) (1999), 387–425).

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