Geometry and topology · Oct 6, 2026

Finite Smith–Toda complexes at every height

For every n ≥ 0, constructs a finite Smith–Toda spectrum at a prime p depending on n, with Brown–Peterson homology BP∗/(p,v1,…,vn)BP_*/(p,v_1,\ldots,v_n) and the canonical comodule structure. Thus Smith–Toda complexes exist at every height when the prime may vary; an explicit example realizes V(4)V(4) at p = 1009.

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