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On the motivic Adams conjecture

Alexey Ananyevskiy (LMU Munich)

The classical Adams conjecture established with different methods by Quillen, Sullivan and Becker and Gottlieb says for which vector bundles the associated sphere bundles are fiber stably homotopy equivalent. I will address the same question in the setting of the motivic homotopy theory. Our approach involves some torsion bounds on the motivic stable stems, motivic mod k Dold theorem, a version of the Brown's trick and explicit manipulations with A1-degrees. In the talk I will introduce all the necessary ingredients and show how one may combine them to obtain the result. This is a joint work with Elden Elmanto, Oliver Röndigs and Maria Yakerson.