For every n ≥ 0, constructs a finite Smith–Toda spectrum at a prime p depending on n, with Brown–Peterson homology \(BP_*/(p,v_1,\ldots,v_n)\) and the canonical comodule structure. Thus Smith–Toda complexes exist at every height when the prime may vary; an explicit example realizes \(V(4)\) at p = 1009.
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In Finite Smith–Toda Complexes at Varying Primes, 23 September 2026
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For every integer n\geq0, there exist a prime p and a finite p-local spectrum X such that
as graded \BP_*\BP-comodules, with the canonical quotient coaction and generator in degree zero.
In A finite Smith–Toda complex V(4) at the prime 1009, 23 September 2026
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At p=1009 there is a finite p-local spectrum X and an isomorphism
of graded BP_*BP-comodules, with the canonical quotient comodule on the right and its generator in degree zero.
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Why this passage is shown
Theorem 1.1
In Finite Smith–Toda Complexes at Varying Primes, 23 September 2026
Why this passage is shown
Theorem 1.1
In A finite Smith–Toda complex V(4) at the prime 1009, 23 September 2026