The unit map of the algebraic special linear cobordism spectrum
Abstract
In joint work with Elmanto, Hoyois, Khan and Sosnilo, we computed infinite $\mathbb{P}^1$loop spaces of motivic Thom spectra, using the technique of framed correspondences. This result allows us to express nonnegative $\mathbb{G}_m$homotopy groups of motivic Thom spectra in terms of geometric generators and relations. Using this explicit description, we show that the unit map of the algebraic special linear cobordism spectrum induces an isomorphism on $\mathbb{G}_m$homotopy sheaves.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.03859
 Bibcode:
 2019arXiv190803859Y
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology
 EPrint:
 Final version, accepted for publication by the Journal of the Institute of Mathematics of Jussieu