1. CMB 1999 (vol 42 pp. 129)
|Hecke Operations and the Adams $E_2$-Term Based on Elliptic Cohomology |
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
Categories:55N20, 55N22, 55T15, 11F11, 11F25
2. CMB 1998 (vol 41 pp. 20)
|A new cohomological criterion for the $p$-nilpotence of groups |
Let $G$ be a finite group, $H$ a copy of its $p$-Sylow subgroup, and $\kn$ the $n$-th Morava $K$-theory at $p$. In this paper we prove that the existence of an isomorphism between $K(n)^\ast(BG)$ and $K(n)^\ast(BH)$ is a sufficient condition for $G$ to be $p$-nilpotent.