Computations of the Adams-Novikov E ₂-term

Abstract

The author introduces the notion of a minimal resolution for BP _* BP-comodules, and gives an effective algorithm to produce minimal resolutions. This produces the data needed in the work [3] for studying motivic stable stems up to stem 90.

Keywords

Stable homotopy / Adams-Novikov spectral sequence / Hopf algebroid

References

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[2] Gheorghe, B., Wang, G. Z. and Xu, Z. L., The special fiber of the motivic deformation of the stable homotopy category is algebraic, Acta Mathematica, to appear.

[3] Isaksen, D. C., Wang, G. Z. and Xu, Z. L., More stable stems, arXiv:2001.04511, 2020.

[4] Miller H R, Ravenel D C, Wilson W S. Periodic phenomena in the Adams-Novikov spectral sequence. Annals of Mathematics, 1977, 106: 469-516

[5] Novikov, S. P., The methods of algebraic topology from viewpoint of cobordism theory, Izv. Akad. Nauk SSSR, Ser. Mat., 31(4), 1967.

[6] Ravenel D C. Complex cobordism and stable homotopy groups of spheres, 1986, Orlando, FL: Academic Press, Inc

[7] Wang, G. Z. and Xu, Z. L., The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra, arXiv:1601.02185, 2016.