OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
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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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 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.
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We construct a Smith–Toda complex V(4) at the prime 1009. It is an ordinary finite 1009-local spectrum whose Brown–Peterson homology is BP_*/(1009,v_1,v_2,v_3,v_4), with its canonical comodule structure and generator in degree zero.
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