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

Szymik, Markus¹

¹Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, 7491 Trondheim, Norway

Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3717-3743

Résumé

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 Fp, although the converse is clearly true, and that MO is not a polynomial algebra over S∕∕2.

Détail

DOI : 10.2140/agt.2014.14.3717

Classification : 55P43, 13A35, 55P20, 55P42
Keywords: commutative $\mathbb{S}$–algebra, characteristic p, unoriented bordism

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