The homogeneous spectrum of Milnor–Witt K-theory

For any field F   (of characteristic not equal to 2), we determine the Zariski spectrum of homogeneous prime ideals in K⁎MW(F), the Milnor–Witt K-theory ring of F. As a corollary, we recover Lorenz and Leicht's classical result on prime ideals in the Witt ring of F. Our computation can be seen as a first step in Balmer's program for studying the tensor triangular geometry of the stable motivic homotopy category.