Topology Seminar: Kyle Ormsby

In Balmer's framework of tensor triangular geometry, the prime thick tensor ideals in a tensor triangulated category C form a space which admits a continuous map to the Zariski spectrum Spec^h(End_u(1)) of homogeneous prime ideals in the graded endomorphism ring of the unit object.  (Here the grading is induced by an element u of the Picard group of C.)  If C is the stable motivic homotopy category and u is the punctured affine line, then this endomorphism ring is the Milnor-Witt K-theory ring of the base field.  I will describe work by my student, Riley Thornton, which completely determines the homogeneous Zariski spectrum of Milnor-Witt K-theory in terms of the orderings on the base field.  I will then comment on work in progress which uses the structure of this spectrum to study the thick subcategories of the stable motivic homotopy category.