Commutative 𝕊–algebras of prime characteristics and applications to unoriented bordism

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 $H F_{p}$ , although the converse is clearly true, and that $MO$ is not a polynomial algebra over $S ∕ ∕ 2$ .

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Keywords

commutative $\mathbb{S}$–algebra, characteristic p, unoriented bordism

Mathematical Subject Classification 2010

Primary: 55P43

Secondary: 13A35, 55P20, 55P42

References

Publication

Received: 14 May 2014

Accepted: 3 June 2014

Published: 15 January 2015

Authors

Markus Szymik
Department of Mathematical Sciences NTNU Norwegian University of Science and Technology 7491 Trondheim Norway

Volume 14, issue 6 (2014)

Markus Szymik

Abstract