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 $BP_*/(p,v_1,\ldots,v_n)$ 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.
released 2026-09-23 | 1 theorem · 35 lemmas · 51 proofs · 25,601 words |
PLAY LEVEL 1 »(pdf)
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.
released 2026-09-23 | 1 theorem · 19 lemmas · 35 proofs · 18,133 words |
PLAY LEVEL 2 »(pdf)
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.