#### Volume 13, issue 5 (2013)

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Preorientations of the derived motivic multiplicative group

### Jens Hornbostel

Algebraic & Geometric Topology 13 (2013) 2667–2712
##### 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 $K\phantom{\rule{0.3em}{0ex}}$–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
##### Publication
Received: 22 March 2012
Revised: 2 April 2013
Accepted: 4 April 2013
Published: 9 July 2013
##### Authors
 Jens Hornbostel Fachbereich C Mathematik und Informatik Bergische Universität Wuppertal Gaußstrasse 20 D-42119 Wuppertal Germany http://www2.math.uni-wuppertal.de/~hornbost/