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 non-negative ${\mathbb{G}}_m$-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.

Final version, accepted for publication by the Journal of the Institute of Mathematics of Jussieu

References in corpus (6)

• Modules over algebraic cobordism
• On the effectivity of spectra representing motivic cohomology theories
• MW-motivic complexes
• Framed correspondences and the zeroth stable motivic homotopy group in odd characteristic
• A comparison theorem for MW-motivic cohomology
• Nilpotence in normed MGL-modules

Cited by in corpus (3)

• On the infinite loop spaces of algebraic cobordism and the motivic sphere
• The geometric diagonal of the special linear algebraic cobordism
• Operations on Milnor-Witt K-theory