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Monday, November 27, 2017

**Abstract:** This talk will be in two (currently unrelated) parts. First I will construct the stable motivic homotopy category by defining the category of GL spectra which is an analogue of the category of orthogonal spectra from topology. I will mention some nice properties of this category and give examples of motivic GL spectra. In the second part of the talk I will introduce the question of nilpotence in motivic homotopy theory. This seems to be a difficult problem since Nishida nilpotence and the Devinatz-Hopkins-Smith theorems do not carry over immediately. I will talk about some approaches that are being used to shed light on these questions.