Abstract:

In his ICM address on motivic homotopy theory Voevodsky introduced the algebraic cobordism spectrum MGL,
mimicking construction of the Thom spectrum in topology. He also proposed a conjecture that the
geometric diagonal of the coefficient ring of this spectrum should have a nice description as the coefficient
ring of the universal formal group law. This was proven over fields of characteristic zero by Morel, Hopkins,
and Hoyois. In this talk I will explain computation of the analogous part of the coefficient ring of the Panin-Walter
special linear algebraic cobordism spectrum MSL, which can be interpreted as “oriented algebraic cobordism”. For
these purposes, I will construct another Thom spectrum that provides a geometric model for the cofiber of multiplication
by the motivic Hopf element on MSL. Topological analogues of this spectrum have been studied by Wall, Conner, and Floyd.