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Tuesday, November 10, 2015

**Abstract:** In the Morel-Voevodsky motivic stable homotopy category over the complex numbers, Marc Levine proved that the motivic stable stems $\pi_{n,0}$ are isomorphic to the topological stable stems $\pi_n^s$. What can we say about the motivic stable stems over fields of positive characteristic? In this talk, we will discuss calculations of the two-complete motivic stable stems over finite fields of odd characteristic using the motivic Adams spectral sequence. For n < 19, we find that after two-completion, $\pi_{n,0} = \pi_n^s + \pi_{n+1}^s$.