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

Szymik, Markus

doi:10.2140/agt.2014.14.3717

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Markus Szymik

Algebraic & Geometric Topology 14 (2014) 3717–3743

DOI: 10.2140/agt.2014.14.3717

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

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)