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# Hecke Operations and the Adams $E_2$-Term Based on Elliptic Cohomology

Published:1999-06-01
Printed: Jun 1999
• Andrew Baker
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## Abstract

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 $\Ext^1$ which combines use of classical Hecke operators and $p$-adic Hecke operators due to Serre.
 Keywords: Adams spectral sequence, elliptic cohomology, Hecke operators
 MSC Classifications: 55N20 - Generalized (extraordinary) homology and cohomology theories 55N22 - Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90] 55T15 - Adams spectral sequences 11F11 - Holomorphic modular forms of integral weight 11F25 - Hecke-Petersson operators, differential operators (one variable)