#### Volume 14, issue 6 (2014)

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Commutative $\mathbb{S}$–algebras of prime characteristics and applications to unoriented bordism

### Markus Szymik

Algebraic & Geometric Topology 14 (2014) 3717–3743
##### Abstract

The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples $\mathbb{S}∕\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}∕p$ for prime numbers $p$. These can be realized as Thom spectra, and therefore relate to other Thom spectra such as the unoriented bordism spectrum $MO$. We compute the Hochschild and André–Quillen invariants of the $\mathbb{S}∕\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}∕p$. Among other applications, we show that $\mathbb{S}∕\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}∕p$ is not a commutative algebra over the Eilenberg–Mac Lane spectrum $H{\mathbb{F}}_{p}$, although the converse is clearly true, and that $MO$ is not a polynomial algebra over $\mathbb{S}∕\phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}∕2$.

##### Keywords
commutative $\mathbb{S}$–algebra, characteristic p, unoriented bordism
##### Mathematical Subject Classification 2010
Primary: 55P43
Secondary: 13A35, 55P20, 55P42