## Algebraic & Geometric Topology

### Preorientations of the derived motivic multiplicative group

Jens Hornbostel

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 13, Number 5 (2013), 2667-2712.

Dates
Revised: 2 April 2013
Accepted: 4 April 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715687

Digital Object Identifier
doi:10.2140/agt.2013.13.2667

Mathematical Reviews number (MathSciNet)
MR3116300

Zentralblatt MATH identifier
1281.55009

#### Citation

Hornbostel, Jens. Preorientations of the derived motivic multiplicative group. Algebr. Geom. Topol. 13 (2013), no. 5, 2667--2712. doi:10.2140/agt.2013.13.2667. https://projecteuclid.org/euclid.agt/1513715687

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#### Corrections

• Jens Hornbostel. Correction to the article Preorientations of the derived motivic multiplicative group. Algebr. Geom. Topol. 18 (2018), no. 2, 1257--1258.