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The structure of the homotopy groups of the motivic sphere spectrum

Kyle Ormsby, Reed College
Thursday, April 4, 2019 - 2:30pm to 3:30pm
LOW 113

The homotopy groups of the motivic sphere spectrum are the invariants governing the universe of (cellular) stable motivic homotopy theory.  I will motivate and construct this bi-graded system of groups over a general base field, and then delve into their structural aspects, focusing on vanishing lines and behavior in the eta-periodic range, where the motivic Hopf map acts as an isomorphism.  I will conclude by discussing a slice spectral sequence approach to the homotopy groups of the eta-periodic motivic sphere (joint with Oliver Röndigs) which provides complete information in case the base field has odd characteristic or cohomological dimension at most one.  This recovers a theorem of Andrews-Miller over C and suggests a "Witt-theoretic image of J pattern" in general.

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