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Quotients of even rings
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abstract
We prove that if $R$ is an $\mathbb{E}_2$-ring with homotopy concentrated in even degrees, and $\{x_j\}$ is any sequence of elements in $\pi_{2*}(R)$, then $R/(x_1,x_2,\cdots)$ admits the structure of an $\mathbb{E}_1$-$R$-algebra. This removes an assumption, common in the literature, that $\{x_j\}$ be a regular sequence.
Forward citations
Cited by 2 Pith papers
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Tensor Nilpotence and the Size of the Bousfield Lattice
For each prime p and integer n, the author builds spectra X_n with X_n^{⊗n} ≠ 0 but X_n^{⊗(n+1)} ≃ 0, refuting the Hovey-Palmieri retract conjecture and showing the Bousfield lattice has 2^{2^{ℵ_0}} elements.
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Syntomic cohomology of truncated Brown--Peterson spectra
For every E1 MU-algebra form of BP⟨n⟩, the mod (p,v1,...,v_{n+1}) syntomic cohomology is computed, yielding redshift, telescope, and Lichtenbaum–Quillen for its algebraic K-theory.
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