A finite Smith–Toda complex V(4) at the prime 1009
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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The Smith-Toda complex V(4) exists for p >= 11arXiv.orgVigleik AngeltveitOct 16, 2026in the index
We show that the Smith-Toda complex V(4) exists for all primes p >= 11. This improves on the recently announced result by OpenAI that V(4) exists at the prime 1009.