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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

The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples Sp 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 Sp. Among other applications, we show that Sp is not a commutative algebra over the Eilenberg–Mac Lane spectrum H Fp, although the converse is clearly true, and that MO is not a polynomial algebra over S2.

commutative $\mathbb{S}$–algebra, characteristic p, unoriented bordism
Mathematical Subject Classification 2010
Primary: 55P43
Secondary: 13A35, 55P20, 55P42
Received: 14 May 2014
Accepted: 3 June 2014
Published: 15 January 2015
Markus Szymik
Department of Mathematical Sciences
NTNU Norwegian University of Science and Technology
7491 Trondheim