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

Published online by Cambridge University Press:  20 November 2018

Andrew Baker
Andrew Baker*
Affiliation:
University of Glasgow Glasgow G12 8QW Scotland, email: [email protected]
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Abstract

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Hecke operators are used to investigate part of the ${{E}_{2}}$-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of $\text{Ex}{{\text{t}}^{1}}$ which combines use of classical Hecke operators and $p$-adic Hecke operators due to Serre.

Keywords

55N2055N2255T1511F1111F25Adams spectral sequenceelliptic cohomologyHecke operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 129 - 138
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Adams, J. F., Stable homotopy and generalised homology. Reprint of the 1974 original, University of Chicago Press, Chicago, 1995.Google Scholar
[2] Baker, A., Elliptic cohomology, p-adic modular forms and Atkin's operator Up. Contemp. Math. 96 (1989), 33–38.Google Scholar
[3] Baker, A., Hecke operators as operations in elliptic cohomology. J. Pure Appl. Algebra 63 (1990), 1–11.Google Scholar
[4] Baker, A., Elliptic genera of level N and elliptic cohomology. J. LondonMath. Soc. 49 (1994), 583–93.Google Scholar
[5] Baker, A., Operations and cooperations in elliptic cohomology, Part I: Generalized modular forms and the cooperation algebra. New York J. Math. 1 (1995), 39–74.Google Scholar
[6] Baker, A., Hecke algebras acting on elliptic cohomology. In: Homotopy theory via algebraic geometry and group representations (Eds. M. Mahowald and S. Priddy), Contemp. Math., to appear.Google Scholar
[7] Clarke, F. and Johnson, K., Cooperations in elliptic homology. In: Adams Memorial Symposium on Algebraic Topology, Vol. 2 (Eds. N. Ray and G.Walker), LondonMath. Soc. Lecture Note Ser. 175 (1992), 131–43.Google Scholar
[8] Gouvea, F. Q., Arithmetic of p-adic modular forms. Lecture Notes in Math. 1304, 1988.Google Scholar
[9] Lang, S., Introduction to modular forms. Springer-Verlag, Berlin, 1995.Google Scholar
[10] Laures, G., The topological q-expansion principle. Preprint.Google Scholar
[11] Serre, J-P., Congruences et formes modulaires (après H. P. F. Swinnerton-Dyer). Sém. Bourbaki 24e Année (1971/2), No. 416; Lecture Notes in Math. 317 (1973), 319–38.Google Scholar
[12] Serre, J-P., Formes modulaires et fonctions zeta p-adiques. Lecture Notes in Math. 350 (1973), 191–268.Google Scholar
[13] Switzer, R. M., Algebraic topology—homotopy and homology. Springer-Verlag, New York-Heidelberg, 1975.Google Scholar