{"id":"openai-math/Finite-Smith-Toda-Complexes-at-Varying-Primes","pdf":"https://github.com/openai/math/blob/main/preprints/Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Finite-Smith-Toda-Complexes-at-Varying-Primes-September-23-2026","tags":["stable-homotopy","chromatic-homotopy","brown-peterson-homology"],"score":0,"title":"Finite Smith–Toda Complexes at Varying Primes","domain":"Topology","family":"308","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"For every nonnegative integer n , we construct a Smith–Toda complex $`V(n)`$ at some prime p depending on n . It is a finite p -local spectrum whose Brown–Peterson homology is $`\\mathrm{BP}_*/(p,v_1,\\ldots,v_n)`$ with its canonical comodule structure and generator in degree zero. Each listed generator is killed to its first power.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Finite Smith–Toda complexes at every height"}