On the infinite loop spaces of algebraic cobordism and the motivic sphere

Bachmann, Tom; Elmanto, Elden; Hoyois, Marc; Khan, Adeel A.; Sosnilo, Vladimir and Yakerson, Maria (2021): On the infinite loop spaces of algebraic cobordism and the motivic sphere. In: Epijournal De Geometrie Algebrique, Vol. 5, 9

Abstract

We obtain geometric models for the infinite loop spaces of the motivic spectra MGL, MSL, and 1 over a field. They are motivically equivalent to Z x Hilb(infinity)(lci)(A(infinity))(+), Z x Hilb(infinity SH6MS) X-or (A(infinity))(+), and Z x Hilb(infinity)(fr),(A(infinity))(+), respectively, where Hilb(d)(lci) (A(n)) (resp. Hilb(d)(or) (A(n)), Hilb(d)(fr)(A(n))) is the Hilbert scheme of lci points (resp. oriented points, framed points) of degree d in A(n) , and + is Quillen's plus construction. Moreover, we show that the plus construction is redundant in positive characteristic.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 2491-6765
• Language: English