Preorientations of the derived motivic multiplicative group

Hornbostel, Jens

doi:10.2140/agt.2013.13.2667

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Preorientations of the derived motivic multiplicative group

Jens Hornbostel

Algebraic & Geometric Topology 13 (2013) 2667–2712

DOI: 10.2140/agt.2013.13.2667

Correction: 10.2140/agt.2018.18.1257

Abstract

We establish several new model structures and Quillen adjunctions both in the classical and in the motivic case for algebras over operads and for modules over strictly commutative ring spectra. As an application, we provide a proof in the language of model categories and symmetric spectra of Lurie’s Theorem that topological complex $K$ –theory represents orientations of the derived multiplicative group. Then we generalize this result to the motivic situation.

Keywords

motivic homotopy theory, motivic operads

Mathematical Subject Classification 2010

Primary: 55P42

Secondary: 18D50, 19D99, 14F42

References

Publication

Received: 22 March 2012

Revised: 2 April 2013

Accepted: 4 April 2013

Published: 9 July 2013

Correction: 12 March 2018

Authors

Jens Hornbostel
Fachbereich C Mathematik und Informatik Bergische Universität Wuppertal Gaußstrasse 20 D-42119 Wuppertal Germany
http://www2.math.uni-wuppertal.de/~hornbost/

Volume 13, issue 5 (2013)