2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77632Let 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.10 pages, AMSLateXAlgebraic Topology55N22 (Primary) 55T15, 55P42 (Secondary)text