Open problems in the motivic stable homotopy theory, I, by Vladimir Voevodsky

In this paper we define the slice filtration on the motivic stable homotopy category which leads to the motivic analogs of the Atiyah-Hirzebruch spectral sequences for the generalized motivic cohomology theories. We formulate a group of conjectures which describe the corresponding Postnikoff towers for the K-theory, algebraic cobordisms and the motivic sphere spectrum. We also discuss the convergence problems.

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