Family 308TopologyNo LeanNot yet digested
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 and the canonical comodule structure. Thus Smith–Toda complexes exist at every height when the prime may vary; an explicit example realizes at p = 1009.
Manuscripts in this family · 2
Finite Smith–Toda Complexes at Varying Primes
Sep 23, 2026·paper.pdf
For every nonnegative integer n, we construct a Smith–Toda complex at some prime p depending on n. It is a finite p-local spectrum whose Brown–Peterson homology is with its canonical comodule structure and generator in degree zero. Each listed generator is killed to its first power.
A finite Smith–Toda complex V(4) at the prime 1009
Sep 23, 2026·paper.pdf
We construct a Smith–Toda complex at the prime 1009. It is an ordinary finite 1009-local spectrum whose Brown–Peterson homology is , with its canonical comodule structure and generator in degree zero.