From $K(n+1)_*(X)$ to $K(n)_*(X)$

Norihiko Minami
2001 Proceedings of the American Mathematical Society  
Let X be a space of finite type. Set q = 2(p − 1) as usual, and define the mod q support of K(n) * (X) by S(X, K(n) Then we show the relation S(X, K(n)) S(X, K(n + 1)) for any finite type space X with K(n + 1) * (X) being sparse. As a special case, we have K(n + 1) odd (X) = 0 =⇒ K(n) odd (X) = 0, and the main theorem of Ravenel, Wilson and Yagita is also generalized in terms of the mod q support.
doi:10.1090/s0002-9939-01-06374-2 fatcat:lcmpxmcsnnathinixkx4mitzoq