Algebraic & Geometric Topology

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

Markus Szymik

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Abstract

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 HFp, although the converse is clearly true, and that MO is not a polynomial algebra over S2.

Article information

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

Dates
Received: 14 May 2014
Accepted: 3 June 2014
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 55P20: Eilenberg-Mac Lane spaces 55P42: Stable homotopy theory, spectra

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

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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