Let p be a prime. The Smith-Toda complex V(k) is a finite spectrum whose
BP-homology is isomorphic to BP_*/(p,v_1,...,v_k). For example, V(-1) is the
sphere spectrum and V(0) the mod p Moore spectrum. In this paper we show that
if p > 5, then V((p+3)/2) does not exist and V((p+1)/2), if it exists, is not a
ring spectrum. The proof uses the new homotopy fixed point spectral sequences
of Hopkins and Miller.Comment: 10 pages, AMSLate