## Algebraic & Geometric Topology

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

Markus Szymik

#### Abstract

The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples $S∕∕p$ 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 $S∕∕p$. Among other applications, we show that $S∕∕p$ is not a commutative algebra over the Eilenberg–Mac Lane spectrum $HFp$, although the converse is clearly true, and that $MO$ is not a polynomial algebra over $S∕∕2$.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 6 (2014), 3717-3743.

Dates
Accepted: 3 June 2014
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513716055

Digital Object Identifier
doi:10.2140/agt.2014.14.3717

Mathematical Reviews number (MathSciNet)
MR3302977

Zentralblatt MATH identifier
1311.55014

#### Citation

Szymik, Markus. Commutative $\mathbb{S}$–algebras of prime characteristics and applications to unoriented bordism. Algebr. Geom. Topol. 14 (2014), no. 6, 3717--3743. doi:10.2140/agt.2014.14.3717. https://projecteuclid.org/euclid.agt/1513716055

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